diff --git a/STL_Extension/include/CGAL/STL_Extension/internal/boost/relaxed_heap.hpp b/STL_Extension/include/CGAL/STL_Extension/internal/boost/relaxed_heap.hpp
index 1da1048916a..e416af439d5 100644
--- a/STL_Extension/include/CGAL/STL_Extension/internal/boost/relaxed_heap.hpp
+++ b/STL_Extension/include/CGAL/STL_Extension/internal/boost/relaxed_heap.hpp
@@ -13,9 +13,9 @@
 // $Id$
 // SPDX-License-Identifier: BSL-1.0
 //
-// NOTE: this file have been taken from boost 1.77 for using
-//       with Modificable_priority_queue
-//       original file is <boost/pending/relaxed_heap.hpp>
+// NOTE: this file has been taken from boost 1.77 to use
+//       with Modificable_priority_queue.
+//       The original file is <boost/pending/relaxed_heap.hpp>
 //
 
 #ifndef BOOST_RELAXED_HEAP_HEADER
diff --git a/Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/edge_collapse.h b/Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/edge_collapse.h
index 749978906cf..16f9d7804e9 100644
--- a/Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/edge_collapse.h
+++ b/Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/edge_collapse.h
@@ -93,8 +93,8 @@ the number of edges effectively removed.
      \cgalParamType{Either `CGAL::Tag_true` or `CGAL::Tag_false`}
      \cgalParamDefault{`CGAL::Tag_false()`}
      \cgalParamExtra{Using a relaxed order will allow the algorithm to use a faster priority queue.
-                     However, if for example a user expects that all elements shorter than a given value to be collapsed,
-                     a relaxed order shall not be used.}
+                     However, the ordering of the priority queue is no longer strict and there is a possibility
+                     that some elements that ought to have been collapsed are not actually collapsed.}
    \cgalParamNEnd
 \cgalNamedParamsEnd
 
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/internal/Edge_collapse.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/internal/Edge_collapse.h
index 2ae57ba2542..18d729c2a9e 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/internal/Edge_collapse.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/internal/Edge_collapse.h
@@ -313,7 +313,6 @@ private:
     CGAL_expensive_assertion(mPQ->contains(h));
 
     mPQ->update(h);
-    data.set_is_in_PQ();
 
     CGAL_assertion(data.is_in_PQ());
     CGAL_expensive_assertion(mPQ->contains(h));