diff --git a/src/db/db/dbAsIfFlatRegion.cc b/src/db/db/dbAsIfFlatRegion.cc
index 4f88ae245..c7927afcf 100644
--- a/src/db/db/dbAsIfFlatRegion.cc
+++ b/src/db/db/dbAsIfFlatRegion.cc
@@ -545,7 +545,7 @@ AsIfFlatRegion::selected_interacting_generic (const Region &other, int mode, boo
     return clone ();
   } else if (max_count < min_count || other.empty ()) {
     //  clear, if b is empty and
-    //   * mode is inside or interacting and inverse is false ("inside" or "interacting")
+    //   * mode is inside, enclosing or interacting and inverse is false ("inside" or "interacting")
     //   * mode is outside and inverse is true ("not outside")
     if ((mode <= 0) != inverse) {
       return new EmptyRegion ();
@@ -586,7 +586,7 @@ AsIfFlatRegion::selected_interacting_generic (const Region &other, int mode, boo
 
     if (mode < 0) {
 
-      //  NOTE: on "inside", the other region must be merged
+      //  NOTE: on "inside" or "enclosing", the other region must be merged
       for (RegionIterator p = other.begin_merged (); ! p.at_end (); ++p) {
         if (p->box ().touches (bbox ())) {
           ep.insert (*p, nstart);
@@ -609,8 +609,8 @@ AsIfFlatRegion::selected_interacting_generic (const Region &other, int mode, boo
 
     //  with counting we need to separate the other polygons by different properties
 
-    //  can only have min_count/max_count in interact mode
-    tl_assert (mode == 0);
+    //  cannot only have min_count/max_count in outside mode
+    tl_assert (mode <= 0);
 
     for (RegionIterator p = other.begin_merged (); ! p.at_end (); ++p) {
       if (p->box ().touches (bbox ())) {
@@ -621,6 +621,9 @@ AsIfFlatRegion::selected_interacting_generic (const Region &other, int mode, boo
 
   }
 
+  //  there should be at least one element to look at for primary
+  tl_assert (nstart > 0);
+
   size_t n = nstart;
   for (RegionIterator p (begin_merged ()); ! p.at_end (); ++p, ++n) {
     if (mode > 0 || p->box ().touches (other.bbox ())) {
@@ -628,7 +631,7 @@ AsIfFlatRegion::selected_interacting_generic (const Region &other, int mode, boo
     }
   }
 
-  db::InteractionDetector id (mode, 0);
+  db::InteractionDetector id (mode, nstart - 1);
   id.set_include_touching (touching);
   db::EdgeSink es;
   ep.process (es, id);
diff --git a/src/db/db/dbAsIfFlatRegion.h b/src/db/db/dbAsIfFlatRegion.h
index 2ec96546b..3d92b1b52 100644
--- a/src/db/db/dbAsIfFlatRegion.h
+++ b/src/db/db/dbAsIfFlatRegion.h
@@ -188,6 +188,16 @@ public:
     return selected_interacting_generic (other, -1, true, true);
   }
 
+  virtual RegionDelegate *selected_enclosing (const Region &other, size_t min_count, size_t max_count) const
+  {
+    return selected_interacting_generic (other, -2, true, false, min_count, max_count);
+  }
+
+  virtual RegionDelegate *selected_not_enclosing (const Region &other, size_t min_count, size_t max_count) const
+  {
+    return selected_interacting_generic (other, -2, true, true, min_count, max_count);
+  }
+
   virtual RegionDelegate *selected_interacting (const Region &other, size_t min_count, size_t max_count) const
   {
     return selected_interacting_generic (other, 0, true, false, min_count, max_count);
@@ -218,14 +228,14 @@ public:
     return selected_interacting_generic (other, true, min_count, max_count);
   }
 
-  virtual RegionDelegate *selected_overlapping (const Region &other) const
+  virtual RegionDelegate *selected_overlapping (const Region &other, size_t min_count, size_t max_count) const
   {
-    return selected_interacting_generic (other, 0, false, false);
+    return selected_interacting_generic (other, 0, false, false, min_count, max_count);
   }
 
-  virtual RegionDelegate *selected_not_overlapping (const Region &other) const
+  virtual RegionDelegate *selected_not_overlapping (const Region &other, size_t min_count, size_t max_count) const
   {
-    return selected_interacting_generic (other, 0, false, true);
+    return selected_interacting_generic (other, 0, false, true, min_count, max_count);
   }
 
   virtual RegionDelegate *pull_inside (const Region &other) const
diff --git a/src/db/db/dbEdgeProcessor.cc b/src/db/db/dbEdgeProcessor.cc
index 8e5836351..25021a0e4 100644
--- a/src/db/db/dbEdgeProcessor.cc
+++ b/src/db/db/dbEdgeProcessor.cc
@@ -628,13 +628,13 @@ bool EdgePolygonOp::selects_edges () const
 // -------------------------------------------------------------------------------
 //  InteractionDetector implementation
 
-InteractionDetector::InteractionDetector (int mode, property_type container_id)
-  : m_mode (mode), m_include_touching (true), m_container_id (container_id)
+InteractionDetector::InteractionDetector (int mode, property_type primary_id)
+  : m_mode (mode), m_include_touching (true), m_last_primary_id (primary_id)
 {
   // .. nothing yet ..
 }
 
-void 
+void
 InteractionDetector::reset ()
 {
   m_wcv_n.clear ();
@@ -675,39 +675,64 @@ InteractionDetector::edge (bool north, bool enter, property_type p)
 
       inside->erase (p);
 
-      if (m_mode != 0) {
-
-        //  the container objects are delivered last of all coincident edges
-        //  (due to prefer_touch == true and the sorting of coincident edges by property id)
-        //  hence every remaining parts count as non-interacting (outside)
-        if (p == m_container_id) {
+      if (m_mode < -1) {
+        //  in enclosing mode report primaries open after a secondary ended as non-interactions: these only partially
+        //  overlap and the outside part qualifies this secondary as non-closing (see "finish")
+        if (p > m_last_primary_id) {
           for (std::set <property_type>::const_iterator i = inside->begin (); i != inside->end (); ++i) {
-            if (*i != m_container_id) {
+            if (*i <= m_last_primary_id) {
+              m_non_interactions.insert (*i);
+            }
+          }
+        }
+      } else if (m_mode != 0) {
+        //  the primary objects are delivered last of all coincident edges
+        //  (due to prefer_touch == true and the sorting of coincident edges by property id)
+        //  hence every remaining parts count as non-interacting (outside)
+        if (p <= m_last_primary_id) {
+          for (std::set <property_type>::const_iterator i = inside->begin (); i != inside->end (); ++i) {
+            if (*i > m_last_primary_id) {
               m_non_interactions.insert (*i);
             }
           }
         }
-
       }
 
     } else if (inside_after > inside_before) {
 
       if (m_mode != 0) {
 
-        //  in inside/outside mode we are only interested in interactions with the container_id property
-        if (p != m_container_id) {
-          //  note that the container parts will be delivered first of all coincident 
-          //  edges hence we can check whether the container is present even for coincident
-          //  edges
-          if (inside->find (m_container_id) != inside->end ()) {
-            m_interactions.insert (std::make_pair (m_container_id, p));
+        //  in enclosing/inside/outside mode we are only interested in interactions with a primary
+        if (p > m_last_primary_id) {
+
+          if (m_mode < -1) {
+            //  enclosing mode: report primaries open when a secondary starts as non-interactions: these only partially
+            //  overlap and the outside part qualifies this secondary as non-closing (see "finish")
+            for (std::set <property_type>::const_iterator i = inside->begin (); i != inside->end (); ++i) {
+              if (*i <= m_last_primary_id) {
+                m_non_interactions.insert (*i);
+              }
+            }
           } else {
-            m_non_interactions.insert (p);
+            //  note that the primary parts will be delivered first of all coincident
+            //  edges hence we can check whether the primary is present even for coincident
+            //  edges
+            bool any = false;
+            for (std::set <property_type>::const_iterator i = inside->begin (); i != inside->end (); ++i) {
+              if (*i <= m_last_primary_id) {
+                any = true;
+                m_interactions.insert (std::make_pair (*i, p));
+              }
+            }
+            if (! any) {
+              m_non_interactions.insert (p);
+            }
           }
+
         } else {
           for (std::set <property_type>::const_iterator i = inside->begin (); i != inside->end (); ++i) {
-            if (*i != m_container_id) {
-              m_interactions.insert (std::make_pair (m_container_id, *i));
+            if (*i > m_last_primary_id) {
+              m_interactions.insert (std::make_pair (p, *i));
             }
           }
         }
@@ -750,14 +775,36 @@ InteractionDetector::compare_ns () const
 void
 InteractionDetector::finish ()
 {
-  if (m_mode < 0) {
+  if (m_mode < -1) {
 
-    //  In inside mode remove those objects which have a non-interaction with the container_id property
-    for (std::set<property_type>::const_iterator p = m_non_interactions.begin (); p != m_non_interactions.end (); ++p) {
-      m_interactions.erase (std::make_pair (m_container_id, *p));
+    //  In enclosing mode remove those objects which have an interaction with a primary having a non-interaction
+    std::set<property_type> secondaries_to_delete;
+    for (std::set<std::pair<property_type, property_type> >::iterator i = m_interactions.begin (); i != m_interactions.end (); ++i) {
+      if (i->first <= m_last_primary_id && m_non_interactions.find (i->first) != m_non_interactions.end ()) {
+        secondaries_to_delete.insert (i->second);
+      }
     }
 
-    m_non_interactions.clear ();
+    for (std::set<std::pair<property_type, property_type> >::iterator i = m_interactions.begin (); i != m_interactions.end (); ) {
+      std::set<std::pair<property_type, property_type> >::iterator ii = i;
+      ++ii;
+      if (i->first <= m_last_primary_id && secondaries_to_delete.find (i->second) != secondaries_to_delete.end ()) {
+        m_interactions.erase (i);
+      }
+      i = ii;
+    }
+
+  } else if (m_mode == -1) {
+
+    //  In inside mode remove those objects which have a non-interaction with a primary
+    for (std::set<std::pair<property_type, property_type> >::iterator i = m_interactions.begin (); i != m_interactions.end (); ) {
+      std::set<std::pair<property_type, property_type> >::iterator ii = i;
+      ++ii;
+      if (i->first <= m_last_primary_id && m_non_interactions.find (i->second) != m_non_interactions.end ()) {
+        m_interactions.erase (i);
+      }
+      i = ii;
+    }
 
   } else if (m_mode > 0) {
 
@@ -768,13 +815,12 @@ InteractionDetector::finish ()
 
     m_interactions.clear ();
     for (std::set<property_type>::const_iterator p = m_non_interactions.begin (); p != m_non_interactions.end (); ++p) {
-      m_interactions.insert (m_interactions.end (), std::make_pair (m_container_id, *p));
+      m_interactions.insert (m_interactions.end (), std::make_pair (m_last_primary_id, *p));
     }
 
-    m_non_interactions.clear ();
-
   }
 
+  m_non_interactions.clear ();
 }
 
 // -------------------------------------------------------------------------------
diff --git a/src/db/db/dbEdgeProcessor.h b/src/db/db/dbEdgeProcessor.h
index d1d000638..40ed4fcce 100644
--- a/src/db/db/dbEdgeProcessor.h
+++ b/src/db/db/dbEdgeProcessor.h
@@ -234,6 +234,7 @@ public:
    *  The mode parameter selects the interaction check mode.
    *  0 is "overlapping". 
    *  -1 will select all polygons inside polygons from the other layer.
+   *  -2 will select all polygons enclosing polygons from the other layer.
    *  +1 will select all polygons outside polygons from the other layer.
    *
    *  In mode -1 and +1, finish () needs to be called before the interactions
@@ -242,16 +243,19 @@ public:
    *  input polygons (property != reference property). In mode +1 these are 
    *  pseudo-interactions, because "outside" by definition means non-interacting.
    *
-   *  Mode -1 (inside) and +1 (outside) requires a single property value for the containing region.
-   *  This property value must be specified in the container_id parameter. 
-   *  For correct operation, the container_id must be the lowest property ID and
-   *  the interacting objects must have higher property id's.
-   *  The reported interactions will be (container_id,polygon_id) even for outside mode.
+   *  Mode -1 (inside) and +1 (outside) requires a property value for the containing (primary) region.
+   *  Property IDs from 0 to the given last primary ID value are considered to belong to
+   *  the primary region.
+   *  This last property ID must be specified in the last_primary_id parameter.
+   *  For correct operation, the secondary input must use property IDs bigger than
+   *  last_primary_id.
+   *  The reported interactions will be (primary_id,polygon_id) even for outside mode.
+   *  For outside mode, the primary_id is always last_primary_id.
    *
-   *  For mode 0, property ids <= container_id are considered to belong to the first
+   *  For mode 0, property ids <= last_primary_id are considered to belong to the first
    *  container and property ids > container_id to the second container.
    */
-  InteractionDetector (int mode = 0, property_type container_id = 0);
+  InteractionDetector (int mode = 0, property_type primary_id = 0);
 
   /**
    *  @brief Sets the "touching" flag
@@ -308,7 +312,7 @@ public:
 private:
   int m_mode;
   bool m_include_touching;
-  property_type m_container_id;
+  property_type m_last_primary_id;
   std::vector <int> m_wcv_n, m_wcv_s;
   std::set <property_type> m_inside_n, m_inside_s;
   std::set<std::pair<property_type, property_type> > m_interactions;
diff --git a/src/db/db/dbEmptyRegion.h b/src/db/db/dbEmptyRegion.h
index b868b95bb..373d3e7f2 100644
--- a/src/db/db/dbEmptyRegion.h
+++ b/src/db/db/dbEmptyRegion.h
@@ -110,14 +110,16 @@ public:
   virtual RegionDelegate *selected_not_outside (const Region &) const { return new EmptyRegion (); }
   virtual RegionDelegate *selected_inside (const Region &) const { return new EmptyRegion (); }
   virtual RegionDelegate *selected_not_inside (const Region &) const { return new EmptyRegion (); }
+  virtual RegionDelegate *selected_enclosing (const Region &, size_t, size_t) const { return new EmptyRegion (); }
+  virtual RegionDelegate *selected_not_enclosing (const Region &, size_t, size_t) const { return new EmptyRegion (); }
   virtual RegionDelegate *selected_interacting (const Region &, size_t, size_t) const { return new EmptyRegion (); }
   virtual RegionDelegate *selected_not_interacting (const Region &, size_t, size_t) const { return new EmptyRegion (); }
   virtual RegionDelegate *selected_interacting (const Edges &, size_t, size_t) const { return new EmptyRegion (); }
   virtual RegionDelegate *selected_not_interacting (const Edges &, size_t, size_t) const { return new EmptyRegion (); }
   virtual RegionDelegate *selected_interacting (const Texts &, size_t, size_t) const { return new EmptyRegion (); }
   virtual RegionDelegate *selected_not_interacting (const Texts &, size_t, size_t) const { return new EmptyRegion (); }
-  virtual RegionDelegate *selected_overlapping (const Region &) const { return new EmptyRegion (); }
-  virtual RegionDelegate *selected_not_overlapping (const Region &) const { return new EmptyRegion (); }
+  virtual RegionDelegate *selected_overlapping (const Region &, size_t, size_t) const { return new EmptyRegion (); }
+  virtual RegionDelegate *selected_not_overlapping (const Region &, size_t, size_t) const { return new EmptyRegion (); }
   virtual RegionDelegate *pull_inside (const Region &) const  { return new EmptyRegion (); }
   virtual RegionDelegate *pull_interacting (const Region &) const  { return new EmptyRegion (); }
   virtual EdgesDelegate *pull_interacting (const Edges &) const  { return new EmptyEdges (); }
diff --git a/src/db/db/dbRegion.h b/src/db/db/dbRegion.h
index 6bb510914..0cf15700f 100644
--- a/src/db/db/dbRegion.h
+++ b/src/db/db/dbRegion.h
@@ -1178,6 +1178,52 @@ public:
     return Region (mp_delegate->selected_not_inside (other));
   }
 
+  /**
+   *  @brief Returns all polygons of this which are enclosing polygons from the other region
+   *
+   *  Merged semantics applies.
+   */
+  Region &select_enclosing (const Region &other, size_t min_count = 1, size_t max_count = std::numeric_limits<size_t>::max ())
+  {
+    set_delegate (mp_delegate->selected_enclosing (other, min_count, max_count));
+    return *this;
+  }
+
+  /**
+   *  @brief Returns all polygons of this which are not enclosing polygons from the other region
+   *
+   *  Merged semantics applies.
+   */
+  Region &select_not_enclosing (const Region &other, size_t min_count = 1, size_t max_count = std::numeric_limits<size_t>::max ())
+  {
+    set_delegate (mp_delegate->selected_not_enclosing (other, min_count, max_count));
+    return *this;
+  }
+
+  /**
+   *  @brief Returns all polygons of this which are enclosing polygons from the other region
+   *
+   *  This method is an out-of-place version of select_enclosing.
+   *
+   *  Merged semantics applies.
+   */
+  Region selected_enclosing (const Region &other, size_t min_count = 1, size_t max_count = std::numeric_limits<size_t>::max ()) const
+  {
+    return Region (mp_delegate->selected_enclosing (other, min_count, max_count));
+  }
+
+  /**
+   *  @brief Returns all polygons of this which are not enclosing polygons from the other region
+   *
+   *  This method is an out-of-place version of select_not_enclosing.
+   *
+   *  Merged semantics applies.
+   */
+  Region selected_not_enclosing (const Region &other, size_t min_count = 1, size_t max_count = std::numeric_limits<size_t>::max ()) const
+  {
+    return Region (mp_delegate->selected_not_enclosing (other, min_count, max_count));
+  }
+
   /**
    *  @brief Selects all polygons of this region which overlap or touch polygons from the other region
    *
@@ -1329,9 +1375,9 @@ public:
    *
    *  Merged semantics applies.
    */
-  Region &select_overlapping (const Region &other)
+  Region &select_overlapping (const Region &other, size_t min_count = 1, size_t max_count = std::numeric_limits<size_t>::max ())
   {
-    set_delegate (mp_delegate->selected_overlapping (other));
+    set_delegate (mp_delegate->selected_overlapping (other, min_count, max_count));
     return *this;
   }
 
@@ -1340,9 +1386,9 @@ public:
    *
    *  Merged semantics applies.
    */
-  Region &select_not_overlapping (const Region &other)
+  Region &select_not_overlapping (const Region &other, size_t min_count = 1, size_t max_count = std::numeric_limits<size_t>::max ())
   {
-    set_delegate (mp_delegate->selected_not_overlapping (other));
+    set_delegate (mp_delegate->selected_not_overlapping (other, min_count, max_count));
     return *this;
   }
 
@@ -1353,9 +1399,9 @@ public:
    *
    *  Merged semantics applies.
    */
-  Region selected_overlapping (const Region &other) const
+  Region selected_overlapping (const Region &other, size_t min_count = 1, size_t max_count = std::numeric_limits<size_t>::max ()) const
   {
-    return Region (mp_delegate->selected_overlapping (other));
+    return Region (mp_delegate->selected_overlapping (other, min_count, max_count));
   }
 
   /**
@@ -1365,9 +1411,9 @@ public:
    *
    *  Merged semantics applies.
    */
-  Region selected_not_overlapping (const Region &other) const
+  Region selected_not_overlapping (const Region &other, size_t min_count = 1, size_t max_count = std::numeric_limits<size_t>::max ()) const
   {
-    return Region (mp_delegate->selected_not_overlapping (other));
+    return Region (mp_delegate->selected_not_overlapping (other, min_count, max_count));
   }
 
   /**
diff --git a/src/db/db/dbRegionDelegate.h b/src/db/db/dbRegionDelegate.h
index 87c9720da..4bcfcbd16 100644
--- a/src/db/db/dbRegionDelegate.h
+++ b/src/db/db/dbRegionDelegate.h
@@ -351,14 +351,16 @@ public:
   virtual RegionDelegate *selected_not_outside (const Region &other) const = 0;
   virtual RegionDelegate *selected_inside (const Region &other) const = 0;
   virtual RegionDelegate *selected_not_inside (const Region &other) const = 0;
+  virtual RegionDelegate *selected_enclosing (const Region &other, size_t min_count, size_t max_count) const = 0;
+  virtual RegionDelegate *selected_not_enclosing (const Region &other, size_t min_count, size_t max_count) const = 0;
   virtual RegionDelegate *selected_interacting (const Region &other, size_t min_count, size_t max_count) const = 0;
   virtual RegionDelegate *selected_not_interacting (const Region &other, size_t min_count, size_t max_count) const = 0;
   virtual RegionDelegate *selected_interacting (const Edges &other, size_t min_count, size_t max_count) const = 0;
   virtual RegionDelegate *selected_not_interacting (const Edges &other, size_t min_count, size_t max_count) const = 0;
   virtual RegionDelegate *selected_interacting (const Texts &other, size_t min_count, size_t max_count) const = 0;
   virtual RegionDelegate *selected_not_interacting (const Texts &other, size_t min_count, size_t max_count) const = 0;
-  virtual RegionDelegate *selected_overlapping (const Region &other) const = 0;
-  virtual RegionDelegate *selected_not_overlapping (const Region &other) const = 0;
+  virtual RegionDelegate *selected_overlapping (const Region &other, size_t min_count, size_t max_count) const = 0;
+  virtual RegionDelegate *selected_not_overlapping (const Region &other, size_t min_count, size_t max_count) const = 0;
   virtual RegionDelegate *pull_inside (const Region &other) const = 0;
   virtual RegionDelegate *pull_interacting (const Region &other) const = 0;
   virtual EdgesDelegate *pull_interacting (const Edges &other) const = 0;
diff --git a/src/db/db/dbRegionLocalOperations.cc b/src/db/db/dbRegionLocalOperations.cc
index e2998637e..fdef45336 100644
--- a/src/db/db/dbRegionLocalOperations.cc
+++ b/src/db/db/dbRegionLocalOperations.cc
@@ -466,7 +466,9 @@ void interacting_local_operation<TS, TI, TR>::compute_local (db::Layout * /*layo
     ep.insert (subject, n);
   }
 
-  db::InteractionDetector id (m_mode, 0);
+  tl_assert (nstart > 0);
+
+  db::InteractionDetector id (m_mode, nstart - 1);
   id.set_include_touching (m_touching);
   db::EdgeSink es;
   ep.process (es, id);
diff --git a/src/db/db/gsiDeclDbCompoundOperation.cc b/src/db/db/gsiDeclDbCompoundOperation.cc
index cef6d37ba..7a162b28b 100644
--- a/src/db/db/gsiDeclDbCompoundOperation.cc
+++ b/src/db/db/gsiDeclDbCompoundOperation.cc
@@ -83,6 +83,19 @@ static db::CompoundRegionOperationNode *new_overlapping (db::CompoundRegionOpera
   }
 }
 
+static db::CompoundRegionOperationNode *new_enclosing (db::CompoundRegionOperationNode *a, db::CompoundRegionOperationNode *b, bool inverse, size_t min_count, size_t max_count)
+{
+  //  TODO: is this correct?
+  if (a->result_type () != db::CompoundRegionOperationNode::Region) {
+    throw tl::Exception ("Primary input for interaction compound operation must be of Region type");
+  }
+  if (b->result_type () == db::CompoundRegionOperationNode::Region) {
+    return new db::CompoundRegionInteractOperationNode (a, b, -2, false, inverse, min_count, max_count);
+  } else {
+    throw tl::Exception ("Secondary input for enclosing compound operation must be of Region type");
+  }
+}
+
 static db::CompoundRegionOperationNode *new_inside (db::CompoundRegionOperationNode *a, db::CompoundRegionOperationNode *b, bool inverse)
 {
   //  TODO: is this correct?
@@ -281,6 +294,9 @@ Class<db::CompoundRegionOperationNode> decl_CompoundRegionOperationNode ("db", "
   gsi::constructor ("new_overlapping", &new_overlapping, gsi::arg ("a"), gsi::arg ("b"), gsi::arg ("inverse", false), gsi::arg ("min_count", size_t (0)), gsi::arg ("max_count", std::numeric_limits<size_t>::max (), "unlimited"),
     "@brief Creates a node representing an overlapping selection operation between the inputs.\n"
   ) +
+  gsi::constructor ("new_enclosing", &new_enclosing, gsi::arg ("a"), gsi::arg ("b"), gsi::arg ("inverse", false), gsi::arg ("min_count", size_t (0)), gsi::arg ("max_count", std::numeric_limits<size_t>::max (), "unlimited"),
+    "@brief Creates a node representing an inside selection operation between the inputs.\n"
+  ) +
   gsi::constructor ("new_inside", &new_inside, gsi::arg ("a"), gsi::arg ("b"), gsi::arg ("inverse", false),
     "@brief Creates a node representing an inside selection operation between the inputs.\n"
   ) +
diff --git a/src/db/db/gsiDeclDbRegion.cc b/src/db/db/gsiDeclDbRegion.cc
index 07eb2fd27..a71f871f9 100644
--- a/src/db/db/gsiDeclDbRegion.cc
+++ b/src/db/db/gsiDeclDbRegion.cc
@@ -1406,6 +1406,42 @@ Class<db::Region> decl_Region (decl_dbShapeCollection, "db", "Region",
     "This operator adds the polygons of the other region to self. "
     "This usually creates unmerged regions and polygons may overlap. Use \\merge if you want to ensure the result region is merged.\n"
   ) + 
+  method ("enclosing", &db::Region::selected_enclosing, gsi::arg ("other"), gsi::arg ("min_count", size_t (1)), gsi::arg ("max_count", size_t (std::numeric_limits<size_t>::max ()), "unlimited"),
+    "@brief Returns the polygons of this region which are completely enclosing polygons from the other region\n"
+    "\n"
+    "@return A new region containing the polygons which are enclosing polygons from the other region\n"
+    "\n"
+    "Merged semantics applies for this method (see \\merged_semantics= of merged semantics)\n"
+    "\n"
+    "This method has been introduced in version 0.27."
+  ) +
+  method ("not_enclosing", &db::Region::selected_not_enclosing, gsi::arg ("other"), gsi::arg ("min_count", size_t (1)), gsi::arg ("max_count", size_t (std::numeric_limits<size_t>::max ()), "unlimited"),
+    "@brief Returns the polygons of this region which are not completely enclosing polygons from the other region\n"
+    "\n"
+    "@return A new region containing the polygons which are not enclosing polygons from the other region\n"
+    "\n"
+    "Merged semantics applies for this method (see \\merged_semantics= of merged semantics)\n"
+    "\n"
+    "This method has been introduced in version 0.27."
+  ) +
+  method ("select_enclosing", &db::Region::select_enclosing, gsi::arg ("other"), gsi::arg ("min_count", size_t (1)), gsi::arg ("max_count", size_t (std::numeric_limits<size_t>::max ()), "unlimited"),
+    "@brief Selects the polygons of this region which are completely enclosing polygons from the other region\n"
+    "\n"
+    "@return The region after the polygons have been selected (self)\n"
+    "\n"
+    "Merged semantics applies for this method (see \\merged_semantics= of merged semantics)\n"
+    "\n"
+    "This method has been introduced in version 0.27."
+  ) +
+  method ("select_not_enclosing", &db::Region::select_not_enclosing, gsi::arg ("other"), gsi::arg ("min_count", size_t (1)), gsi::arg ("max_count", size_t (std::numeric_limits<size_t>::max ()), "unlimited"),
+    "@brief Selects the polygons of this region which are not completely enclosing polygons from the other region\n"
+    "\n"
+    "@return The region after the polygons have been selected (self)\n"
+    "\n"
+    "Merged semantics applies for this method (see \\merged_semantics= of merged semantics)\n"
+    "\n"
+    "This method has been introduced in version 0.27."
+  ) +
   method ("inside", &db::Region::selected_inside, gsi::arg ("other"),
     "@brief Returns the polygons of this region which are completely inside polygons from the other region\n"
     "\n"
@@ -1634,34 +1670,42 @@ Class<db::Region> decl_Region (decl_dbShapeCollection, "db", "Region",
     "\n"
     "This method has been introduced in version 0.27\n"
   ) +
-  method ("overlapping", &db::Region::selected_overlapping, gsi::arg ("other"),
+  method ("overlapping", &db::Region::selected_overlapping, gsi::arg ("other"), gsi::arg ("min_count", size_t (1)), gsi::arg ("max_count", size_t (std::numeric_limits<size_t>::max ()), "unlimited"),
     "@brief Returns the polygons of this region which overlap polygons from the other region\n"
     "\n"
     "@return A new region containing the polygons overlapping polygons from the other region\n"
     "\n"
     "Merged semantics applies for this method (see \\merged_semantics= of merged semantics)\n"
+    "\n"
+    "The count options have been introduced in version 0.27."
   ) + 
-  method ("not_overlapping", &db::Region::selected_not_overlapping, gsi::arg ("other"),
+  method ("not_overlapping", &db::Region::selected_not_overlapping, gsi::arg ("other"), gsi::arg ("min_count", size_t (1)), gsi::arg ("max_count", size_t (std::numeric_limits<size_t>::max ()), "unlimited"),
     "@brief Returns the polygons of this region which do not overlap polygons from the other region\n"
     "\n"
     "@return A new region containing the polygons not overlapping polygons from the other region\n"
     "\n"
     "Merged semantics applies for this method (see \\merged_semantics= of merged semantics)\n"
-  ) + 
-  method ("select_overlapping", &db::Region::select_overlapping, gsi::arg ("other"),
+    "\n"
+    "The count options have been introduced in version 0.27."
+  ) +
+  method ("select_overlapping", &db::Region::select_overlapping, gsi::arg ("other"), gsi::arg ("min_count", size_t (1)), gsi::arg ("max_count", size_t (std::numeric_limits<size_t>::max ()), "unlimited"),
     "@brief Selects the polygons from this region which overlap polygons from the other region\n"
     "\n"
     "@return The region after the polygons have been selected (self)\n"
     "\n"
     "Merged semantics applies for this method (see \\merged_semantics= of merged semantics)\n"
-  ) + 
-  method ("select_not_overlapping", &db::Region::select_not_overlapping, gsi::arg ("other"),
+    "\n"
+    "The count options have been introduced in version 0.27."
+  ) +
+  method ("select_not_overlapping", &db::Region::select_not_overlapping, gsi::arg ("other"), gsi::arg ("min_count", size_t (1)), gsi::arg ("max_count", size_t (std::numeric_limits<size_t>::max ()), "unlimited"),
     "@brief Selects the polygons from this region which do not overlap polygons from the other region\n"
     "\n"
     "@return The region after the polygons have been selected (self)\n"
     "\n"
     "Merged semantics applies for this method (see \\merged_semantics= of merged semantics)\n"
-  ) + 
+    "\n"
+    "The count options have been introduced in version 0.27."
+  ) +
   method ("pull_inside", &db::Region::pull_inside, gsi::arg ("other"),
     "@brief Returns all polygons of \"other\" which are inside polygons of this region\n"
     "The \"pull_...\" methods are similar to \"select_...\" but work the opposite way: they "
diff --git a/src/drc/drc/built-in-macros/_drc_layer.rb b/src/drc/drc/built-in-macros/_drc_layer.rb
index b54ef5689..14ca2ce0b 100644
--- a/src/drc/drc/built-in-macros/_drc_layer.rb
+++ b/src/drc/drc/built-in-macros/_drc_layer.rb
@@ -1418,10 +1418,90 @@ CODE
     # This method is available for polygon, edge and edge pair layers. An alias
     # is "\join". See there for a description of the function.
    
+    # %DRC%
+    # @name enclosing
+    # @brief Selects shapes or regions of self which completely enclose one or more shapes from the other region
+    # @synopsis layer.enclosing(other)
+    # @synopsis layer.enclosing(other, min_count)
+    # @synopsis layer.enclosing(other, min_count, max_count)
+    # @synopsis layer.enclosing(other, min_count .. max_count)
+    # This method selects all shapes or regions from self which enclose shapes from the other
+    # region. Unless self is in raw mode (see \raw), coherent regions are selected from self, 
+    # otherwise individual shapes are selected.
+    # It returns a new layer containing the selected shapes. A version which modifies self
+    # is \select_enclosing.
+    #
+    # This method is available for polygon and edge layers. Edges can be selected
+    # with respect to other edges or polygons.
+    #
+    # The following image shows the effect of the "enclosing" method:
+    #
+    # @table
+    #   @tr 
+    #     @td @img(/images/drc_enclosing.png) @/td
+    #   @/tr
+    # @/table
+    #
+    # A range of counts can be specified. If so, the shape from the primary layer is 
+    # only selected when enclosing a given number of shapes from the other layer.
+    # For the interpretation of the count see \interacting.
+    
+    # %DRC%
+    # @name not_enclosing
+    # @brief Selects shapes or regions of self which do not enclose one or more shapes from the other region
+    # @synopsis layer.not_enclosing(other)
+    # @synopsis layer.not_enclosing(other, min_count)
+    # @synopsis layer.not_enclosing(other, min_count, max_count)
+    # @synopsis layer.not_enclosing(other, min_count .. max_count)
+    # This method selects all shapes or regions from self which do not enclose shapes from the other
+    # region. Unless self is in raw mode (see \raw), coherent regions are selected from self, 
+    # otherwise individual shapes are selected. This method returns the inverse of \enclosing
+    # and provides the same options.
+    #
+    # This method is available for polygon and edge layers. Edges can be selected
+    # with respect to other edges or polygons.
+    # It returns a new layer containing the selected shapes. A version which modifies self
+    # is \select_not_enclosing.
+    
+    # %DRC%
+    # @name select_enclosing
+    # @brief Selects shapes or regions of self which completely enclose one or more shapes from the other region
+    # @synopsis layer.select_enclosing(other)
+    # @synopsis layer.select_enclosing(other, min_count)
+    # @synopsis layer.select_enclosing(other, min_count, max_count)
+    # @synopsis layer.select_enclosing(other, min_count .. max_count)
+    # This method selects all shapes or regions from self which overlap shapes from the other
+    # region. Unless self is in raw mode (see \raw), coherent regions are selected from self, 
+    # otherwise individual shapes are selected.
+    # It modifies self to contain the selected shapes. A version which does not modify self
+    # is \enclosing.
+    #
+    # This method is available for polygon and edge layers. Edges can be selected
+    # with respect to other edges or polygons.
+    
+    # %DRC%
+    # @name select_not_enclosing
+    # @brief Selects shapes or regions of self which do not enclose one or more shapes from the other region
+    # @synopsis layer.select_not_enclosing(other)
+    # @synopsis layer.select_not_enclosing(other, min_count)
+    # @synopsis layer.select_not_enclosing(other, min_count, max_count)
+    # @synopsis layer.select_not_enclosing(other, min_count .. max_count)
+    # This method selects all shapes or regions from self which do not enclose shapes from the other
+    # region. Unless self is in raw mode (see \raw), coherent regions are selected from self, 
+    # otherwise individual shapes are selected. 
+    # It modifies self to contain the selected shapes. A version which does not modify self
+    # is \not_enclosing.
+    #
+    # This method is available for polygon and edge layers. Edges can be selected
+    # with respect to other edges or polygons.
+
     # %DRC%
     # @name overlapping
     # @brief Selects shapes or regions of self which overlap shapes from the other region
     # @synopsis layer.overlapping(other)
+    # @synopsis layer.overlapping(other, min_count)
+    # @synopsis layer.overlapping(other, min_count, max_count)
+    # @synopsis layer.overlapping(other, min_count .. max_count)
     # This method selects all shapes or regions from self which overlap shapes from the other
     # region. Unless self is in raw mode (see \raw), coherent regions are selected from self, 
     # otherwise individual shapes are selected.
@@ -1438,17 +1518,25 @@ CODE
     #     @td @img(/images/drc_overlapping.png) @/td
     #   @/tr
     # @/table
+    #
+    # A range of counts can be specified. If so, the shape from the primary layer is 
+    # only selected when overlapping a given number of shapes from the other layer.
+    # For the interpretation of the count see \interacting.
     
     # %DRC%
     # @name not_overlapping
     # @brief Selects shapes or regions of self which do not overlap shapes from the other region
     # @synopsis layer.not_overlapping(other)
+    # @synopsis layer.not_overlapping(other, min_count)
+    # @synopsis layer.not_overlapping(other, min_count, max_count)
+    # @synopsis layer.not_overlapping(other, min_count .. max_count)
     # This method selects all shapes or regions from self which do not overlap shapes from the other
     # region. Unless self is in raw mode (see \raw), coherent regions are selected from self, 
-    # otherwise individual shapes are selected.
+    # otherwise individual shapes are selected. This method will return the inverse of \overlapping
+    # and provides the same options.
     #
-    # The "not_overlapping" method is equivalent to the \outside method. It is provided
-    # as an alias for consistency.
+    # The "not_overlapping" method is similar to the \outside method. However, "outside" does 
+    # not provide the option to specify counts.
     #
     # This method is available for polygon and edge layers. Edges can be selected
     # with respect to other edges or polygons.
@@ -1459,6 +1547,9 @@ CODE
     # @name select_overlapping
     # @brief Selects shapes or regions of self which overlap shapes from the other region
     # @synopsis layer.select_overlapping(other)
+    # @synopsis layer.select_overlapping(other, min_count)
+    # @synopsis layer.select_overlapping(other, min_count, max_count)
+    # @synopsis layer.select_overlapping(other, min_count .. max_count)
     # This method selects all shapes or regions from self which overlap shapes from the other
     # region. Unless self is in raw mode (see \raw), coherent regions are selected from self, 
     # otherwise individual shapes are selected.
@@ -1472,6 +1563,9 @@ CODE
     # @name select_not_overlapping
     # @brief Selects shapes or regions of self which do not overlap shapes from the other region
     # @synopsis layer.select_not_overlapping(other)
+    # @synopsis layer.select_not_overlapping(other, min_count)
+    # @synopsis layer.select_not_overlapping(other, min_count, max_count)
+    # @synopsis layer.select_not_overlapping(other, min_count .. max_count)
     # This method selects all shapes or regions from self which do not overlap shapes from the other
     # region. Unless self is in raw mode (see \raw), coherent regions are selected from self, 
     # otherwise individual shapes are selected. 
@@ -1902,7 +1996,7 @@ CODE
 CODE
     end
 
-    %w(| ^ overlapping not_overlapping inside not_inside outside not_outside in not_in).each do |f| 
+    %w(| ^ inside not_inside outside not_outside in not_in).each do |f| 
       eval <<"CODE"
       def #{f}(other)
         requires_same_type(other, "#{f}")
@@ -1974,7 +2068,34 @@ CODE
 CODE
     end
     
-    %w(overlapping not_overlapping inside not_inside outside not_outside).each do |fi|
+    %w(overlapping not_overlapping enclosing not_enclosing).each do |f| 
+      eval <<"CODE"
+      def #{f}(other, *args)
+        requires_same_type(other, "#{f}")
+        requires_edges_or_region("#{f}")
+        DRCLayer::new(@engine, @engine._tcmd(self.data, 0, self.data.class, :#{f}, other.data, *minmax_count(:#{f}, *args)))
+      end
+CODE
+    end
+
+    %w(overlapping not_overlapping enclosing not_enclosing).each do |fi|
+      f = "select_" + fi
+      # In tiled mode, there are no modifying versions. Emulate using the non-modifying one.
+      eval <<"CODE"
+      def #{f}(other, *args)
+        requires_edges_or_region("#{f}")
+        requires_same_type(other, "#{f}")
+        if @engine.is_tiled?
+          self.data = @engine._tcmd(self.data, 0, self.data.class, :#{fi}, other.data, *minmax_count(:#{fi}, *args))
+          DRCLayer::new(@engine, self.data)
+        else
+          DRCLayer::new(@engine, @engine._tcmd(self.data, 0, self.data.class, :#{f}, other.data, *minmax_count(:#{f}, *args)))
+        end
+      end
+CODE
+    end
+    
+    %w(inside not_inside outside not_outside).each do |fi|
       f = "select_" + fi
       # In tiled mode, there are no modifying versions. Emulate using the non-modifying one.
       eval <<"CODE"
diff --git a/testdata/drc/drcSimpleTests_20.drc b/testdata/drc/drcSimpleTests_20.drc
index c5c803995..7d96f6d6e 100644
--- a/testdata/drc/drcSimpleTests_20.drc
+++ b/testdata/drc/drcSimpleTests_20.drc
@@ -16,6 +16,12 @@ l1.interacting(l2, 1..2).output(102, 0)
 l1.interacting(l2, 2..).output(103, 0)
 l1.interacting(l2, 1, 2).output(104, 0)
 
+l1.overlapping(l2, 1).output(110, 0)
+l1.overlapping(l2, 2).output(111, 0)
+l1.overlapping(l2, 1..2).output(112, 0)
+l1.overlapping(l2, 2..).output(113, 0)
+l1.overlapping(l2, 1, 2).output(114, 0)
+
 l = l1.dup
 l.select_interacting(l2, 1)
 l.output(200, 0)
@@ -32,12 +38,34 @@ l = l1.dup
 l.select_interacting(l2, 1, 2)
 l.output(204, 0)
 
+l = l1.dup
+l.select_overlapping(l2, 1)
+l.output(210, 0)
+l = l1.dup
+l.select_overlapping(l2, 2)
+l.output(211, 0)
+l = l1.dup
+l.select_overlapping(l2, 1..2)
+l.output(212, 0)
+l = l1.dup
+l.select_overlapping(l2, 2..)
+l.output(213, 0)
+l = l1.dup
+l.select_overlapping(l2, 1, 2)
+l.output(214, 0)
+
 l1.not_interacting(l2, 1).output(300, 0)
 l1.not_interacting(l2, 2).output(301, 0)
 l1.not_interacting(l2, 1..2).output(302, 0)
 l1.not_interacting(l2, 2..).output(303, 0)
 l1.not_interacting(l2, 1, 2).output(304, 0)
 
+l1.not_overlapping(l2, 1).output(310, 0)
+l1.not_overlapping(l2, 2).output(311, 0)
+l1.not_overlapping(l2, 1..2).output(312, 0)
+l1.not_overlapping(l2, 2..).output(313, 0)
+l1.not_overlapping(l2, 1, 2).output(314, 0)
+
 l = l1.dup
 l.select_not_interacting(l2, 1)
 l.output(400, 0)
@@ -54,3 +82,19 @@ l = l1.dup
 l.select_not_interacting(l2, 1, 2)
 l.output(404, 0)
 
+l = l1.dup
+l.select_not_overlapping(l2, 1)
+l.output(410, 0)
+l = l1.dup
+l.select_not_overlapping(l2, 2)
+l.output(411, 0)
+l = l1.dup
+l.select_not_overlapping(l2, 1..2)
+l.output(412, 0)
+l = l1.dup
+l.select_not_overlapping(l2, 2..)
+l.output(413, 0)
+l = l1.dup
+l.select_not_overlapping(l2, 1, 2)
+l.output(414, 0)
+
diff --git a/testdata/drc/drcSimpleTests_20.gds b/testdata/drc/drcSimpleTests_20.gds
index 08618beb2..aab1a575c 100644
Binary files a/testdata/drc/drcSimpleTests_20.gds and b/testdata/drc/drcSimpleTests_20.gds differ
diff --git a/testdata/drc/drcSimpleTests_au20.gds b/testdata/drc/drcSimpleTests_au20.gds
index 77c6d5bfc..7607a2253 100644
Binary files a/testdata/drc/drcSimpleTests_au20.gds and b/testdata/drc/drcSimpleTests_au20.gds differ