diff --git a/Intersections_2/test/Intersections_2/test_intersections_2.cpp b/Intersections_2/test/Intersections_2/test_intersections_2.cpp
index f501bf75211..073adae0846 100644
--- a/Intersections_2/test/Intersections_2/test_intersections_2.cpp
+++ b/Intersections_2/test/Intersections_2/test_intersections_2.cpp
@@ -798,9 +798,9 @@ int main()
 {
   CGAL::Set_ieee_double_precision pfr;
 
-  Test< CGAL::Simple_cartesian<typename CGAL::internal::Exact_field_selector<void*>::Type > >().run();
+  Test< CGAL::Simple_cartesian<CGAL::internal::Exact_field_selector<void*>::Type > >().run();
   Test< CGAL::Cartesian<double>   >().run();
-  Test< CGAL::Homogeneous<typename CGAL::internal::Exact_field_selector<void*>::Type > >().run();
+  Test< CGAL::Homogeneous<CGAL::internal::Exact_field_selector<void*>::Type > >().run();
   Test< CGAL::Exact_predicates_inexact_constructions_kernel >().run();
   Test< CGAL::Exact_predicates_exact_constructions_kernel >().run();
 }
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Face_graph_output_builder.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Face_graph_output_builder.h
index ed08eaef152..0dd34e1753b 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Face_graph_output_builder.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/Face_graph_output_builder.h
@@ -579,12 +579,12 @@ public:
           if ( opposite(next(h1, tm1), tm1) == prev(opposite(h1, tm1), tm1) )
           {
             inter_edges_to_remove1.insert(edge(next(h1, tm1),tm1));
-            inter_edges_to_remove1.insert(edge(next(h2, tm2),tm2));
+            inter_edges_to_remove2.insert(edge(next(h2, tm2),tm2));
           }
           if ( opposite(prev(h1, tm1), tm1) == next(opposite(h1, tm1), tm1) )
           {
             inter_edges_to_remove1.insert(edge(prev(h1, tm1), tm1));
-            inter_edges_to_remove1.insert(edge(prev(h2, tm2), tm2));
+            inter_edges_to_remove2.insert(edge(prev(h2, tm2), tm2));
           }
         }
         // same but for h2
@@ -598,12 +598,12 @@ public:
           if ( opposite(next(h2, tm2), tm2) == prev(opposite(h2, tm2), tm2) )
           {
             inter_edges_to_remove1.insert(edge(next(h1, tm1),tm1));
-            inter_edges_to_remove1.insert(edge(next(h2, tm2),tm2));
+            inter_edges_to_remove2.insert(edge(next(h2, tm2),tm2));
           }
           if ( opposite(prev(h2, tm2), tm2) == next(opposite(h2, tm2), tm2) )
           {
             inter_edges_to_remove1.insert(edge(prev(h1, tm1), tm1));
-            inter_edges_to_remove1.insert(edge(prev(h2, tm2), tm2));
+            inter_edges_to_remove2.insert(edge(prev(h2, tm2), tm2));
           }
         }
       }
@@ -611,9 +611,15 @@ public:
         ++epp_it;
     }
     for(edge_descriptor ed : inter_edges_to_remove1)
+    {
+      put(marks_on_input_edges.ecm1, ed, false);
       intersection_edges1.erase(ed);
+    }
     for(edge_descriptor ed : inter_edges_to_remove2)
+    {
+      put(marks_on_input_edges.ecm2, ed, false);
       intersection_edges2.erase(ed);
+    }
 
     // (1) Assign a patch id to each facet indicating in which connected
     // component limited by intersection edges of the surface they are.
diff --git a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Basic_predicates_C2.h b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Basic_predicates_C2.h
index fab693cce20..6eb2fd2e803 100644
--- a/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Basic_predicates_C2.h
+++ b/Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Basic_predicates_C2.h
@@ -143,8 +143,11 @@ public:
   static
   FT to_ft(const Sqrt_3& x)
   {
-    FT sqrt_e = compute_sqrt( to_ft(x.e()), FT_Has_sqrt() );
-    FT sqrt_f = compute_sqrt( to_ft(x.f()), FT_Has_sqrt() );
+    // If the number type does not offer a square root, x.e() and x.f() (which are of type sqrt_1)
+    // might be negative after (approximately) evaluating them. Taking the max sanitize these values
+    // to ensure that we do not take the square root of a negative number.
+    FT sqrt_e = compute_sqrt( (std::max)(FT(0), to_ft(x.e())), FT_Has_sqrt() );
+    FT sqrt_f = compute_sqrt( (std::max)(FT(0), to_ft(x.f())), FT_Has_sqrt() );
     FT sqrt_ef = sqrt_e * sqrt_f;
     return to_ft(x.a()) + to_ft(x.b()) * sqrt_e
       + to_ft(x.c()) * sqrt_f + to_ft(x.d()) * sqrt_ef;