diff --git a/src/V3Randomize.cpp b/src/V3Randomize.cpp
index 0390e3cbc..c920cc1cb 100644
--- a/src/V3Randomize.cpp
+++ b/src/V3Randomize.cpp
@@ -438,26 +438,16 @@ class RandomizeMarkVisitor final : public VNVisitor {
 
         if (nodep->varp()->lifetime().isStatic()) m_staticRefs.emplace(nodep);
 
-        if (!nodep->varp()->rand().isRandomizable()) return;
-        for (AstNode* backp = nodep; backp != m_constraintExprGenp && !backp->user1();
-             backp = backp->backp())
-            backp->user1(true);
+        if (nodep->varp()->rand().isRandomizable()) nodep->user1(true);
     }
     void visit(AstMemberSel* nodep) override {
         if (!m_constraintExprGenp) return;
-        if (VN_IS(nodep->fromp(), LambdaArgRef)) {
-            if (!nodep->varp()->rand().isRandomizable()) return;
-            for (AstNode* backp = nodep; backp != m_constraintExprGenp && !backp->user1();
-                 backp = backp->backp())
-                backp->user1(true);
-        }
-    }
-    void visit(AstArraySel* nodep) override {
-        if (!m_constraintExprGenp) return;
-        for (AstNode* backp = nodep; backp != m_constraintExprGenp && !backp->user1();
-             backp = backp->backp())
-            backp->user1(true);
         iterateChildrenConst(nodep);
+        // Member select are randomized when both object and member are marked as rand.
+        // Variable references in with clause are converted to member selects and their from() is
+        // of type AstLambdaArgRef. They are randomized too.
+        const bool randObject = nodep->fromp()->user1() || VN_IS(nodep->fromp(), LambdaArgRef);
+        nodep->user1(randObject && nodep->varp()->rand().isRandomizable());
     }
     void visit(AstNodeModule* nodep) override {
         VL_RESTORER(m_modp);
@@ -473,6 +463,14 @@ class RandomizeMarkVisitor final : public VNVisitor {
         iterateChildrenConst(nodep);
     }
 
+    void visit(AstNodeExpr* nodep) override {
+        iterateChildrenConst(nodep);
+        if (!m_constraintExprGenp) return;
+        nodep->user1((nodep->op1p() && nodep->op1p()->user1())
+                     || (nodep->op2p() && nodep->op2p()->user1())
+                     || (nodep->op3p() && nodep->op3p()->user1())
+                     || (nodep->op4p() && nodep->op4p()->user1()));
+    }
     void visit(AstNode* nodep) override { iterateChildrenConst(nodep); }
 
 public:
@@ -735,6 +733,12 @@ class ConstraintExprVisitor final : public VNVisitor {
         handle.relink(indexp);
         editSMT(nodep, nodep->fromp(), indexp);
     }
+    void visit(AstMemberSel* nodep) override {
+        if (nodep->user1()) {
+            nodep->v3warn(CONSTRAINTIGN, "Global constraints ignored (unsupported)");
+        }
+        editFormat(nodep);
+    }
     void visit(AstSFormatF* nodep) override {}
     void visit(AstStmtExpr* nodep) override {}
     void visit(AstConstraintIf* nodep) override {
diff --git a/test_regress/t/t_constraint_state.v b/test_regress/t/t_constraint_state.v
index 799dea166..f89f2819a 100644
--- a/test_regress/t/t_constraint_state.v
+++ b/test_regress/t/t_constraint_state.v
@@ -4,12 +4,50 @@
 // any use, without warranty, 2023 by Antmicro Ltd.
 // SPDX-License-Identifier: CC0-1.0
 
+
+`define check_rand(cl, field, cond) \
+begin \
+   longint prev_result; \
+   int ok = 0; \
+   if (!bit'(cl.randomize())) $stop; \
+   prev_result = longint'(field); \
+   if (!(cond)) $stop; \
+   repeat(9) begin \
+      longint result; \
+      if (!bit'(cl.randomize())) $stop; \
+      result = longint'(field); \
+      if (!(cond)) $stop; \
+      if (result != prev_result) ok = 1; \
+      prev_result = result; \
+   end \
+   if (ok != 1) $stop; \
+end
+
+class Foo;
+   int x;
+endclass
+
+class Bar;
+   rand int y;
+endclass
+
 class Packet;
    rand int rf;
    int state;
+   rand int a;
+   rand Foo foo;
+   Bar bar;
 
-   constraint c { rf == state; }
+   constraint c1 { rf == state; }
+   constraint c2 { a > foo.x; a < bar.y; }
 
+   function new(int s, int x, int y);
+      state = s;
+      foo = new;
+      foo.x = x;
+      bar = new;
+      bar.y = y;
+   endfunction
 endclass
 
 module t (/*AUTOARG*/);
@@ -19,12 +57,15 @@ module t (/*AUTOARG*/);
    int v;
 
    initial begin
-      p = new;
-      p.state = 123;
+      p = new(123, 10, 20);
       v = p.randomize();
       if (v != 1) $stop;
       if (p.rf != 123) $stop;
 
+      `check_rand(p, p.a, p.a > 10 && p.a < 20)
+      if (p.foo.x != 10) $stop;
+      if (p.bar.y != 20) $stop;
+
       p.state = 234;
       v = p.randomize();
       if (v != 1) $stop;
diff --git a/test_regress/t/t_randomize_method_types_unsup.out b/test_regress/t/t_randomize_method_types_unsup.out
index 4b53e95ef..4dd60a0a9 100644
--- a/test_regress/t/t_randomize_method_types_unsup.out
+++ b/test_regress/t/t_randomize_method_types_unsup.out
@@ -1,17 +1,20 @@
-%Warning-CONSTRAINTIGN: t/t_randomize_method_types_unsup.v:17:17: Unsupported: randomizing this expression, treating as state
-   17 |       dynarr[1].size < 10;
+%Warning-CONSTRAINTIGN: t/t_randomize_method_types_unsup.v:23:17: Unsupported: randomizing this expression, treating as state
+   23 |       dynarr[1].size < 10;
       |                 ^~~~
                         ... For warning description see https://verilator.org/warn/CONSTRAINTIGN?v=latest
                         ... Use "/* verilator lint_off CONSTRAINTIGN */" and lint_on around source to disable this message.
-%Warning-CONSTRAINTIGN: t/t_randomize_method_types_unsup.v:21:9: Size constraint combined with element constraint may not work correctly
+%Warning-CONSTRAINTIGN: t/t_randomize_method_types_unsup.v:27:9: Size constraint combined with element constraint may not work correctly
                                                                : ... note: In instance 't'
-   21 |       q.size < 5;
+   27 |       q.size < 5;
       |         ^~~~
-%Error-UNSUPPORTED: t/t_randomize_method_types_unsup.v:11:13: Unsupported: random member variable with the type of the containing class
+%Warning-CONSTRAINTIGN: t/t_randomize_method_types_unsup.v:31:10: Global constraints ignored (unsupported)
+   31 |      foo.x < y;
+      |          ^
+%Error-UNSUPPORTED: t/t_randomize_method_types_unsup.v:15:13: Unsupported: random member variable with the type of the containing class
                                                             : ... note: In instance 't'
-   11 |    rand Cls cls;
+   15 |    rand Cls cls;
       |             ^~~
-%Warning-CONSTRAINTIGN: t/t_randomize_method_types_unsup.v:33:43: Unsupported: randomizing this expression, treating as state
-   33 |       res = obj.randomize() with { dynarr.size > 2; };
+%Warning-CONSTRAINTIGN: t/t_randomize_method_types_unsup.v:43:43: Unsupported: randomizing this expression, treating as state
+   43 |       res = obj.randomize() with { dynarr.size > 2; };
       |                                           ^~~~
 %Error: Exiting due to
diff --git a/test_regress/t/t_randomize_method_types_unsup.v b/test_regress/t/t_randomize_method_types_unsup.v
index b68abf141..f100eeac9 100644
--- a/test_regress/t/t_randomize_method_types_unsup.v
+++ b/test_regress/t/t_randomize_method_types_unsup.v
@@ -4,12 +4,18 @@
 // any use, without warranty, 2020 by Wilson Snyder.
 // SPDX-License-Identifier: CC0-1.0
 
+class Foo;
+   rand int x;
+endclass
+
 class Cls;
    rand int assocarr[string];
    rand int dynarr[][];
    rand int q[$];
    rand Cls cls;
    rand int i;
+   rand Foo foo;
+   rand int y;
    int st;
    constraint dynsize {
       dynarr.size < 20;
@@ -21,6 +27,9 @@ class Cls;
       q.size < 5;
       q[i] < 10;
    }
+   constraint global_constraint {
+     foo.x < y;
+  }
 endclass
 
 module t (/*AUTOARG*/);
@@ -29,6 +38,7 @@ module t (/*AUTOARG*/);
 
    initial begin
       obj = new;
+      obj.foo = new;
       res = obj.randomize();
       res = obj.randomize() with { dynarr.size > 2; };
    end