diff --git a/include/mp/flat/constr_keeper.h b/include/mp/flat/constr_keeper.h
index 41b61c05f..28393b2ee 100644
--- a/include/mp/flat/constr_keeper.h
+++ b/include/mp/flat/constr_keeper.h
@@ -980,7 +980,15 @@ class ConstraintKeeper final
       cons_[i].con_.SetName(vn[i].MakeCurrentName());
   }
 
-	/// ForEachActive().
+  /// Copy names to ValueNodes
+  void CopyNames2ValueNodes() {
+    auto& vn = GetValueNode().GetStrVec();
+    assert(vn.size()==cons_.size());
+    for (auto i=vn.size(); i--; )
+      vn[i] = std::string(cons_[i].con_.name());
+  }
+
+  /// ForEachActive().
   /// Deletes every constraint where fn() returns true.
 	template <class Fn>
 	void ForEachActive(Fn fn) {
diff --git a/include/mp/flat/converter.h b/include/mp/flat/converter.h
index ccad7aeff..879c02d02 100644
--- a/include/mp/flat/converter.h
+++ b/include/mp/flat/converter.h
@@ -539,6 +539,9 @@ class FlatConverter :
     if (var_names_.size()) {
       /// Check that constr / obj names are present too?
       GetValuePresolver().CleanUpNameNodes();
+      // They are at top level of the reformulation tree
+      TransferNames2Node((SOS1Constraint*)nullptr);
+      TransferNames2Node((SOS2Constraint*)nullptr);
       auto vm = GetValuePresolver().
           PresolveNames({
                           {var_names_},
@@ -557,6 +560,12 @@ class FlatConverter :
     }
   }
 
+  template <class Con>
+  void TransferNames2Node(Con* pcon) {
+    auto& ck = GetConstraintKeeper(pcon);
+    ck.CopyNames2ValueNodes();
+  }
+
   /// Fill model traits for license check.
   /// To be called after ConvertModel().
   /// KEEP THIS UP2DATE.
diff --git a/include/mp/valcvt-node.h b/include/mp/valcvt-node.h
index 1afd4309d..fca26fb3b 100644
--- a/include/mp/valcvt-node.h
+++ b/include/mp/valcvt-node.h
@@ -208,9 +208,12 @@ class ValueNode {
   /// Retrieve whole vector<VCString&>&
   operator const std::vector<VCString>& () const { return vStr_; }
 
-  /// Retrieve whole vector<VCString&>&
+  /// Retrieve whole const vector<VCString&>&
   const std::vector<VCString>& GetStrVec() const { return vStr_; }
 
+  /// Retrieve whole vector<VCString&>&
+  std::vector<VCString>& GetStrVec() { return vStr_; }
+
 
   /////////////////////// Access individual values ///////////////////////