diff --git a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/CMakeLists.txt b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/CMakeLists.txt
index 988f875425e..0ae9468f45c 100644
--- a/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/CMakeLists.txt
+++ b/Surface_mesh_parameterization/examples/Surface_mesh_parameterization/CMakeLists.txt
@@ -24,21 +24,19 @@ if(TARGET CGAL::Eigen3_support)
     if(SuiteSparse_FOUND)
       include_directories(${SuiteSparse_INCLUDE_DIRS})
     endif(SuiteSparse_FOUND)
-  else(NOT SuiteSparse_FOUND)
-    include(${USE_SuiteSparse})
   endif(NOT SuiteSparse_FOUND)
 
   if(SuiteSparse_FOUND)
-    if(SuiteSparse_UMFPACK_FOUND)
+    if(SuiteSparse_UMFPACK_FOUND OR TARGET SuiteSparse::umfpack)
       message(STATUS "SuiteSparse_LIBS: ${SuiteSparse_LIBRARIES}")
       message(STATUS "Orbifold Tutte Embeddings will use UmfPackLU")
       add_definitions(-DEIGEN_DONT_ALIGN_STATICALLY)
-      add_definitions(-DCGAL_SMP_USE_SPARSESUITE_SOLVERS)
+      add_definitions(-DCGAL_SMP_USE_SUITESPARSE_SOLVERS)
     else()
-      message(STATUS "NOTICE: The example `orbifold.cpp` will be compiled without the Sparsesuite library and UmfPack. Try setting SuiteSparse_UMF_INCLUDE_DIR and at least one of SuiteSparse_UMFPACK_LIBRARY_RELEASE and SuiteSparse_UMFPACK_LIBRARY_DEBUG to you UMFPACK installation.")
+      message(STATUS "NOTICE: The example `orbifold.cpp` will be compiled without the SuiteSparse library and UmfPack. Try setting SuiteSparse_UMF_INCLUDE_DIR and at least one of SuiteSparse_UMFPACK_LIBRARY_RELEASE and SuiteSparse_UMFPACK_LIBRARY_DEBUG to you UMFPACK installation.")
     endif()
   else(SuiteSparse_FOUND)
-    message(STATUS "NOTICE: The example `orbifold.cpp` will be compiled without the Sparsesuite library.")
+    message(STATUS "NOTICE: The example `orbifold.cpp` will not be compiled without the SuiteSparse library.")
   endif(SuiteSparse_FOUND)
 
   # ------------------------------------------------------------------
diff --git a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/ARAP_parameterizer_3.h b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/ARAP_parameterizer_3.h
index 676d6f951a2..ca3de476091 100644
--- a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/ARAP_parameterizer_3.h
+++ b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/ARAP_parameterizer_3.h
@@ -33,7 +33,7 @@
 
 #if defined(CGAL_EIGEN3_ENABLED)
 #include <CGAL/Eigen_solver_traits.h>
-#ifdef CGAL_SMP_USE_SPARSESUITE_SOLVERS
+#ifdef CGAL_SMP_USE_SUITESPARSE_SOLVERS
 #include <Eigen/UmfPackSupport>
 #endif
 #endif
@@ -154,7 +154,7 @@ namespace Surface_mesh_parameterization {
 ///   CGAL::Eigen_solver_traits<
 ///           Eigen::SparseLU<Eigen_sparse_matrix<double>::EigenType> >
 /// \endcode
-///         Moreover, if SparseSuite solvers are available, which is greatly preferable for speed,
+///         Moreover, if SuiteSparse solvers are available, which is greatly preferable for speed,
 ///         then the default parameter is:
 /// \code
 ///   CGAL::Eigen_solver_traits<
@@ -183,7 +183,7 @@ public:
   typedef typename Default::Get<
     SolverTraits_,
   #if defined(CGAL_EIGEN3_ENABLED)
-    #ifdef CGAL_SMP_USE_SPARSESUITE_SOLVERS
+    #ifdef CGAL_SMP_USE_SUITESPARSE_SOLVERS
       CGAL::Eigen_solver_traits<
         Eigen::UmfPackLU<Eigen_sparse_matrix<double>::EigenType> >
     #else
diff --git a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Orbifold_Tutte_parameterizer_3.h b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Orbifold_Tutte_parameterizer_3.h
index 98bc8dd9eac..c23ce5bf15d 100644
--- a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Orbifold_Tutte_parameterizer_3.h
+++ b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Orbifold_Tutte_parameterizer_3.h
@@ -33,7 +33,7 @@
 
 #if defined(CGAL_EIGEN3_ENABLED)
 #include <CGAL/Eigen_solver_traits.h>
-#ifdef CGAL_SMP_USE_SPARSESUITE_SOLVERS
+#ifdef CGAL_SMP_USE_SUITESPARSE_SOLVERS
 #include <Eigen/UmfPackSupport>
 #endif
 #endif
@@ -368,7 +368,7 @@ bool locate_unordered_cones(const SeamMesh& mesh,
 ///   CGAL::Eigen_solver_traits<
 ///           Eigen::SparseLU<Eigen_sparse_matrix<double>::EigenType> >
 /// \endcode
-///         Moreover, if SparseSuite solvers are available, which is greatly preferable for speed,
+///         Moreover, if SuiteSparse solvers are available, which is greatly preferable for speed,
 ///         then the default parameter is:
 /// \code
 ///   CGAL::Eigen_solver_traits<
@@ -391,7 +391,7 @@ public:
   typedef typename Default::Get<
     SolverTraits_,
   #if defined(CGAL_EIGEN3_ENABLED)
-    #ifdef CGAL_SMP_USE_SPARSESUITE_SOLVERS
+    #ifdef CGAL_SMP_USE_SUITESPARSE_SOLVERS
       CGAL::Eigen_solver_traits<
         Eigen::UmfPackLU<Eigen_sparse_matrix<double>::EigenType> >
     #else