diff --git a/src/db/db/dbTriangle.cc b/src/db/db/dbTriangle.cc
index 867187295..e9289a324 100644
--- a/src/db/db/dbTriangle.cc
+++ b/src/db/db/dbTriangle.cc
@@ -32,19 +32,19 @@ namespace db
 //  Vertex implementation
 
 Vertex::Vertex ()
-  : DPoint (), m_level (0)
+  : DPoint (), m_is_precious (false)
 {
   //  .. nothing yet ..
 }
 
 Vertex::Vertex (const db::DPoint &p)
-  : DPoint (p), m_level (0)
+  : DPoint (p), m_is_precious (false)
 {
   //  .. nothing yet ..
 }
 
 Vertex::Vertex (const Vertex &v)
-  : DPoint (), m_level (0)
+  : DPoint (), m_is_precious (false)
 {
   operator= (v);
 }
@@ -54,13 +54,13 @@ Vertex &Vertex::operator= (const Vertex &v)
   if (this != &v) {
     //  NOTE: edges are not copied!
     db::DPoint::operator= (v);
-    m_level = v.m_level;
+    m_is_precious = v.m_is_precious;
   }
   return *this;
 }
 
 Vertex::Vertex (db::DCoord x, db::DCoord y)
-  : DPoint (x, y), m_level (0)
+  : DPoint (x, y), m_is_precious (false)
 {
   //  .. nothing yet ..
 }
diff --git a/src/db/db/dbTriangle.h b/src/db/db/dbTriangle.h
index 29ff09abb..332d1c695 100644
--- a/src/db/db/dbTriangle.h
+++ b/src/db/db/dbTriangle.h
@@ -74,8 +74,8 @@ public:
 
   bool has_edge (const TriangleEdge *edge) const;
 
-  size_t level () const { return m_level; }
-  void set_level (size_t l) { m_level = l; }
+  void set_is_precious (bool f) { m_is_precious = f; }
+  bool is_precious () const { return m_is_precious; }
 
   std::string to_string (bool with_id = false) const;
 
@@ -102,7 +102,7 @@ private:
   }
 
   edges_type mp_edges;
-  size_t m_level;
+  bool m_is_precious;
 };
 
 /**
diff --git a/src/db/db/dbTriangles.cc b/src/db/db/dbTriangles.cc
index 23710b681..e712abaa2 100644
--- a/src/db/db/dbTriangles.cc
+++ b/src/db/db/dbTriangles.cc
@@ -1484,7 +1484,7 @@ Triangles::create_constrained_delaunay (const db::Polygon &p, const std::vector<
   clear ();
 
   for (auto v = vertexes.begin (); v != vertexes.end (); ++v) {
-    insert_point (trans * *v);
+    insert_point (trans * *v)->set_is_precious (true);
   }
 
   std::vector<std::vector<db::Vertex *> > edge_contours;
@@ -1499,7 +1499,7 @@ Triangles::create_constrained_delaunay (const db::DPolygon &p, const std::vector
   clear ();
 
   for (auto v = vertexes.begin (); v != vertexes.end (); ++v) {
-    insert_point (trans * *v);
+    insert_point (trans * *v)->set_is_precious (true);
   }
 
   std::vector<std::vector<db::Vertex *> > edge_contours;
@@ -1724,7 +1724,7 @@ Triangles::refine (const TriangulateParameters &parameters)
               for (auto e = (*v)->begin_edges (); e != (*v)->end_edges () && ! has_segment; ++e) {
                 has_segment = (*e)->is_segment ();
               }
-              if (! has_segment) {
+              if (! has_segment && ! (*v)->is_precious ()) {
                 to_delete.push_back (*v);
               }
             }
diff --git a/src/db/unit_tests/dbTriangleTests.cc b/src/db/unit_tests/dbTriangleTests.cc
index 439eb1c65..4d0eb9e78 100644
--- a/src/db/unit_tests/dbTriangleTests.cc
+++ b/src/db/unit_tests/dbTriangleTests.cc
@@ -54,9 +54,6 @@ TEST(Vertex_basic)
 
   v = db::Vertex (db::DPoint (2, 3));
   EXPECT_EQ (v.to_string (), "(2, 3)");
-
-  v.set_level (42);
-  EXPECT_EQ (v.level (), size_t (42));
 }
 
 static std::string edges_from_vertex (const db::Vertex &v)
diff --git a/src/db/unit_tests/dbTrianglesTests.cc b/src/db/unit_tests/dbTrianglesTests.cc
index c3855ce29..df7c5e357 100644
--- a/src/db/unit_tests/dbTrianglesTests.cc
+++ b/src/db/unit_tests/dbTrianglesTests.cc
@@ -1000,3 +1000,79 @@ TEST(triangulate_issue1996)
   EXPECT_GT (tri.num_triangles (), size_t (128000));
   EXPECT_LT (tri.num_triangles (), size_t (132000));
 }
+
+TEST(triangulate_with_vertexes)
+{
+  db::Point contour[] = {
+    db::Point (0, 0),
+    db::Point (0, 100),
+    db::Point (1000, 100),
+    db::Point (1000, 0)
+  };
+
+  db::Polygon poly;
+  poly.assign_hull (contour + 0, contour + sizeof (contour) / sizeof (contour[0]));
+
+  double dbu = 0.001;
+
+  db::Triangles::TriangulateParameters param;
+  param.min_b = 0.0;
+  param.max_area = 0.0;
+
+  std::vector<db::Point> vertexes;
+
+  TestableTriangles tri;
+  db::CplxTrans trans = db::DCplxTrans (dbu) * db::CplxTrans (db::Trans (db::Point () - poly.box ().center ()));
+  tri.triangulate (poly, param, trans);
+
+  EXPECT_EQ (tri.to_string (), "((-0.5, -0.05), (-0.5, 0.05), (0.5, 0.05)), ((0.5, -0.05), (-0.5, -0.05), (0.5, 0.05))");
+
+  vertexes.clear ();
+
+  //  outside vertexes are ignored, but lead to a different triangulation
+  vertexes.push_back (db::Point (50, 150));
+  tri.triangulate (poly, vertexes, param, trans);
+
+  EXPECT_EQ (tri.to_string (), "((-0.5, -0.05), (-0.133333333333, 0.05), (0.5, -0.05)), ((0.5, 0.05), (0.5, -0.05), (-0.133333333333, 0.05)), ((-0.133333333333, 0.05), (-0.5, -0.05), (-0.5, 0.05))");
+
+  for (auto v = vertexes.begin (); v != vertexes.end (); ++v) {
+    auto *vp = tri.find_vertex_for_point (trans * *v);
+    EXPECT_EQ (vp, 0);
+  }
+
+  vertexes.clear ();
+  vertexes.push_back (db::Point (50, 50));
+  tri.triangulate (poly, vertexes, param, trans);
+
+  EXPECT_EQ (tri.to_string (), "((-0.45, 0), (-0.5, -0.05), (-0.5, 0.05)), ((0.5, 0.05), (-0.45, 0), (-0.5, 0.05)), ((-0.45, 0), (0.5, -0.05), (-0.5, -0.05)), ((-0.45, 0), (0.5, 0.05), (0.5, -0.05))");
+
+  for (auto v = vertexes.begin (); v != vertexes.end (); ++v) {
+    auto *vp = tri.find_vertex_for_point (trans * *v);
+    if (! vp) {
+      tl::warn << "Vertex not present in output: " << v->to_string ();
+      EXPECT_EQ (1, 0);
+    }
+  }
+
+  //  aggressive triangulation
+  param.min_b = 1.0;
+  param.max_area = 20 * 20 * dbu * dbu;
+
+  tri.triangulate (poly, vertexes, param, trans);
+
+  EXPECT_GT (tri.num_triangles (), size_t (380));
+  EXPECT_LT (tri.num_triangles (), size_t (400));
+
+  for (auto t = tri.begin (); t != tri.end (); ++t) {
+    EXPECT_LE (t->area (), param.max_area);
+    EXPECT_GE (t->b (), param.min_b);
+  }
+
+  for (auto v = vertexes.begin (); v != vertexes.end (); ++v) {
+    auto *vp = tri.find_vertex_for_point (trans * *v);
+    if (! vp) {
+      tl::warn << "Vertex not present in output: " << v->to_string ();
+      EXPECT_EQ (1, 0);
+    }
+  }
+}