diff --git a/opm/grid/cpgrid/CpGridData.cpp b/opm/grid/cpgrid/CpGridData.cpp
index 92a2b24c0..da9939b93 100644
--- a/opm/grid/cpgrid/CpGridData.cpp
+++ b/opm/grid/cpgrid/CpGridData.cpp
@@ -587,7 +587,7 @@ struct Cell2PointsDataHandle
         const auto& points = globalCell2Points_[i];
         std::ranges::for_each(points,
                               [&buffer, this](const int& point)
-                              { buffer.write(globalIds_.id(EntityRep<3>(point, true))); });
+                              { buffer.write(globalIds_.idLevelZero(EntityRep<3>(point, true))); });
         for (const auto& point: globalAdditionalPointIds_[i])
         {
             buffer.write(point);
@@ -707,7 +707,7 @@ struct SparseTableDataHandle
         const auto& entries = global_[t.index()];
         std::ranges::for_each(entries,
                               [&buffer, this](const DataType& i)
-                              { buffer.write(globalIds_.id(EntityRep<3>(i, true))); });
+                              { buffer.write(globalIds_.idLevelZero(EntityRep<3>(i, true))); });
     }
     template<class B, class T>
     void scatter(B& buffer, const T& t, std::size_t )
@@ -779,7 +779,7 @@ struct OrientedEntityTableDataHandle
             std::ranges::for_each(entries,
                                   [&buffer, this](const ToEntity& i)
                                   {
-                                      int id = globalIds_->id(i);
+                                      int id = globalIds_->idLevelZero(i);
                                       if (!i.orientation()) {
                                           id = ~id;
                                       }
@@ -853,8 +853,9 @@ struct IndexSet2IdSet
         for (const auto& entry: indexSet)
             map_[entry.local()] = entry.global();
     }
-    template<class T>
-    int id(const T& t) const
+
+    template<int dim>
+    int idLevelZero(const EntityRep<dim>& t) const
     {
         return map_[t.index()];
     }
@@ -1371,7 +1372,7 @@ std::vector<std::set<int> > computeAdditionalFacePoints(const std::vector<std::a
                 const auto candidate = std::ranges::find(points, point);
                 if (candidate == points.end()) {
                     // point is not a corner of the cell
-                    additionalFacePoints[c].insert(globalIds.id(EntityRep<3>(point,true)));
+                    additionalFacePoints[c].insert(globalIds.idLevelZero(EntityRep<3>(point,true)));
                 }
             }
     }
@@ -1475,7 +1476,7 @@ std::map<int,int> computeCell2Point(const CpGrid& grid,
         createInterfaceList<true>(procCellLists, globalCell2Points,
                                   globalAdditionalPoints,
                                   [&globalIds](int i){
-                                      return globalIds.id(EntityRep<3>(i, true));
+                                      return globalIds.idLevelZero(EntityRep<3>(i, true));
                                   },
                                   globalMap2Local,
                                   pointInterfaces[procCellLists.first]);
diff --git a/opm/grid/cpgrid/Entity.hpp b/opm/grid/cpgrid/Entity.hpp
index ce716e691..f60e23bc0 100644
--- a/opm/grid/cpgrid/Entity.hpp
+++ b/opm/grid/cpgrid/Entity.hpp
@@ -57,6 +57,41 @@ namespace Dune
 namespace cpgrid
 {
 
+template <int codim>
+class Entity;
+
+namespace Impl {
+// Forward declaration of traits class for codimensions.
+template <int codim>
+struct CodimTraits;
+
+// Specialization of traits class for codimension 0 (cells).
+template<>
+struct CodimTraits<0>
+{
+    using Entity = ::Dune::cpgrid::Entity<0>;
+};
+
+#if DUNE_VERSION_LT(DUNE_GRID, 2, 11)
+// Specialization of traits class for codimension 1 (faces).
+// This is only needed for DUNE < 2.11, as the face entity type was needed for the VTK writer, which was fixed in DUNE 2.11.
+// See: https://gitlab.dune-project.org/core/dune-grid/-/merge_requests/793
+template<>
+struct CodimTraits<1>
+{
+    using Entity = ::Dune::cpgrid::Entity<1>;
+};
+#endif
+
+// Specialization of traits class for codimension 3 (vertices).
+template<>
+struct CodimTraits<3>
+{
+    using Entity = ::Dune::cpgrid::Entity<3>;
+};
+
+}
+
 template<int,int> class Geometry;
 template<int,PartitionIteratorType> class Iterator;
 class IntersectionIterator;
@@ -93,11 +128,7 @@ class Entity : public EntityRep<codim>
 
     /** \brief Export supported entity types */
     template <int cd>
-    struct Codim
-    {
-        using Entity = ::Dune::cpgrid::Entity<cd>;
-    };
-
+    using Codim = typename Impl::CodimTraits<cd>;
 
     typedef cpgrid::Geometry<3-codim,3> Geometry;
     typedef Geometry LocalGeometry;
@@ -387,7 +418,7 @@ unsigned int Entity<codim>::subEntities ( const unsigned int cc ) const
             return 8;
         }
     }
-    return 0;
+    DUNE_THROW(NotImplemented, "subEntities not implemented for this codimension");
 }
 
 template <int codim>
diff --git a/opm/grid/cpgrid/Indexsets.cpp b/opm/grid/cpgrid/Indexsets.cpp
index 1ea159312..efbeec40f 100644
--- a/opm/grid/cpgrid/Indexsets.cpp
+++ b/opm/grid/cpgrid/Indexsets.cpp
@@ -48,8 +48,6 @@ IndexSet::IndexType IndexSet::subIndex(const cpgrid::Entity<0>& e, int i, unsign
 {
     switch(cc) {
     case 0: return index(e.subEntity<0>(i));
-    case 1: return index(e.subEntity<1>(i));
-    // case 2: return index(e.subEntity<2>(i)); // Not supported in this grid
     case 3: return index(e.subEntity<3>(i));
     default: OPM_THROW(std::runtime_error,
                        "Codimension " + std::to_string(cc) + " not supported.");
@@ -60,8 +58,6 @@ IdSet::IdType IdSet::subId(const cpgrid::Entity<0>& e, int i, int cc) const
 {
     switch (cc) {
     case 0: return id(e.subEntity<0>(i));
-    case 1: return id(e.subEntity<1>(i));
-    // case 2: return id(e.subEntity<2>(i)); // Not supported in this grid
     case 3: return id(e.subEntity<3>(i));
     default: OPM_THROW(std::runtime_error,
                        "Cannot get subId of codimension " + std::to_string(cc));
@@ -75,8 +71,6 @@ LevelGlobalIdSet::IdType LevelGlobalIdSet::subId(const cpgrid::Entity<0>& e, int
 
     switch (cc) {
     case 0: return id(e.subEntity<0>(i));
-        //case 1: return id(*e.subEntity<1>(i));
-        //case 2: return id(*e.subEntity<2>(i));
     case 3: return id(e.subEntity<3>(i));
     default: OPM_THROW(std::runtime_error,
                        "Cannot get subId of codimension " + std::to_string(cc));
diff --git a/opm/grid/cpgrid/Indexsets.hpp b/opm/grid/cpgrid/Indexsets.hpp
index c80211c40..8e1b4910f 100644
--- a/opm/grid/cpgrid/Indexsets.hpp
+++ b/opm/grid/cpgrid/Indexsets.hpp
@@ -38,6 +38,7 @@ along with OPM.  If not, see <http://www.gnu.org/licenses/>.
 
 #include <dune/geometry/type.hh>
 #include <opm/common/ErrorMacros.hpp>
+#include "Entity.hpp"
 #include "GlobalIdMapping.hpp"
 #include "Intersection.hpp"
 
@@ -62,11 +63,8 @@ namespace Dune
             static constexpr int dimension = 3;
 
             /** \brief Export supported entity types */
-            template <int cc>
-            struct Codim
-            {
-              typedef cpgrid::Entity< cc > Entity;
-            };
+            template <int cd>
+            using Codim = typename Impl::CodimTraits<cd>;
 
             /// @brief
             /// @todo Doc me!
@@ -208,11 +206,8 @@ namespace Dune
             static constexpr int dimension = 3;
 
             /** \brief Export supported entity types */
-            template <int cc>
-            struct Codim
-            {
-                using Entity = ::Dune::cpgrid::Entity<cc>;
-            };
+            template <int cd>
+            using Codim = typename Impl::CodimTraits<cd>;
 
             explicit IdSet(const CpGridData& grid)
                 : grid_(grid)
@@ -224,13 +219,11 @@ namespace Dune
             {
                 if constexpr (cd == 0)
                     return computeId_cell(e);
-                else if constexpr (cd == 1)
-                    return computeId(e);
                 else if constexpr (cd == 3)
                     return computeId_point(e);
                 else
                     static_assert(AlwaysFalse<index_constant<cd>>::value,
-                                  "IdSet::id not implemented for codims other thatn 0, 1, and 3.");
+                                  "IdSet::id not implemented for codims other than 0, and 3.");
             }
 
             template<class EntityType>
@@ -240,11 +233,14 @@ namespace Dune
             }
 
             template<int codim>
-            IdType id(const cpgrid::EntityRep<codim>& e) const
+            IdType idLevelZero(const cpgrid::EntityRep<codim>& e) const
             {
                 return computeId(e);
             }
 
+            template<int codim>
+            IdType idLevelZero(const Entity<codim>& e) const = delete;
+
             /// return id of intersection (here face number)
             IdType id( const cpgrid::Intersection& intersection ) const
             {
@@ -377,11 +373,8 @@ namespace Dune
             static constexpr int dimension = 3;
 
             /** \brief Export supported entity types */
-            template <int cc>
-            struct Codim
-            {
-                using Entity = ::Dune::cpgrid::Entity<cc>;
-            };
+            template <int cd>
+            using Codim = typename Impl::CodimTraits<cd>;
 
             void swap(std::vector<int>& cellMapping,
                       std::vector<int>& faceMapping,
@@ -414,14 +407,17 @@ namespace Dune
             }
 
             template<int codim>
-            IdType id(const EntityRep<codim>& e) const
+            IdType idLevelZero(const EntityRep<codim>& e) const
             {
                 if(idSet_)
-                    return idSet_->id(e);
+                    return idSet_->idLevelZero(e);
                 else
                     return this->template getMapping<codim>()[e.index()];
             }
 
+            template<int codim>
+            IdType idLevelZero(const Entity<codim>& e) const = delete;
+
             template<class EntityType>
             IdType id(const EntityType& e) const
             {
@@ -493,10 +489,7 @@ namespace Dune
 
         /** \brief Export supported entity types */
         template <int cd>
-        struct Codim
-        {
-            using Entity = ::Dune::cpgrid::Entity<cd>;
-        };
+        using Codim = typename Impl::CodimTraits<cd>;
 
         explicit GlobalIdSet(const CpGridData& view);
 
diff --git a/tests/cpgrid/distribution_test.cpp b/tests/cpgrid/distribution_test.cpp
index c00d26075..f06bb703d 100644
--- a/tests/cpgrid/distribution_test.cpp
+++ b/tests/cpgrid/distribution_test.cpp
@@ -500,8 +500,6 @@ BOOST_AUTO_TEST_CASE(compareWithSequential)
                 using namespace Dune::cpgrid;
                 auto face = grid.cellFace(eIt->index(), f);
                 auto seqFace = seqGrid.cellFace(seqEIt->index(), f);
-                BOOST_REQUIRE(idSet.id(Dune::createEntity<1>(grid, face, true)) ==
-                              seqIdSet.id(Dune::createEntity<1>(seqGrid, seqFace, true)));
                 int vertices = grid.numFaceVertices(face);
                 BOOST_REQUIRE(vertices == seqGrid.numFaceVertices(seqFace));
                 for (int v = 0; v < vertices; ++v)
@@ -579,11 +577,11 @@ BOOST_AUTO_TEST_CASE(PartitionTest)
         }
     }
     MPI_Barrier(MPI_COMM_WORLD);
-    
+
     if (size > 2)
     {
         MPI_Comm_free(&twocom);
-    }    
+    }
 #endif
 }
 
@@ -638,7 +636,7 @@ BOOST_AUTO_TEST_CASE(PartitionTestWithCorners)
             }
             std::cout<<"done interior "<<(int)Dune::InteriorEntity<<" overlap "<<(int)Dune::OverlapEntity
                      <<" border "<<(int)Dune::BorderEntity<<" front "<<(int)Dune::FrontEntity<<std::endl;
-            
+
             BOOST_CHECK(cells_per_part_type.size() == 2);
             BOOST_CHECK(cells_per_part_type[Dune::InteriorEntity] == 4);
             BOOST_CHECK(cells_per_part_type[Dune::OverlapEntity] == 8);
@@ -659,14 +657,14 @@ BOOST_AUTO_TEST_CASE(PartitionTestWithCorners)
             BOOST_CHECK(points_per_part_type[Dune::BorderEntity] == 14);
             BOOST_CHECK(points_per_part_type[Dune::OverlapEntity] == 6);
             BOOST_CHECK(points_per_part_type[Dune::FrontEntity] == 16);
-        }         
+        }
     }
     MPI_Barrier(MPI_COMM_WORLD);
-    
+
     if (size > 2)
     {
         MPI_Comm_free(&twocom);
-    }    
+    }
 #endif
 }
 
diff --git a/tests/cpgrid/lgr/id_entity_entityrep_test.cpp b/tests/cpgrid/lgr/id_entity_entityrep_test.cpp
index c10933238..c6da59d83 100644
--- a/tests/cpgrid/lgr/id_entity_entityrep_test.cpp
+++ b/tests/cpgrid/lgr/id_entity_entityrep_test.cpp
@@ -86,7 +86,7 @@ std::string coincideString(bool coincide)
 template<typename IdSet, typename EntityRep>
 auto idRep(const IdSet& idSet, const EntityRep& entityRep)
 {
-    return idSet.id(entityRep);
+    return idSet.idLevelZero(entityRep);
 }
 
 void entityRepIndexAndEntityIndexCoincide(const Dune::CpGrid& grid)