diff --git a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS.cmake b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS.cmake
index ca241472d..be7cd2e73 100644
--- a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS.cmake
+++ b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS.cmake
@@ -36,9 +36,9 @@ if ( DEFINED BLAS_LIBRARIES OR DEFINED BLAS_INCLUDE_DIRS )
     # User supplied variables for libraries and/or include directories.
     # Use them as-is.
     if ( SUITESPARSE_USE_64BIT_BLAS )
-        set ( SuiteSparse_BLAS_integer "int64_t" )
+        include ( SuiteSparseBLAS64 )
     else ( )
-        set ( SuiteSparse_BLAS_integer "int32_t" )
+        include ( SuiteSparseBLAS32 )
     endif ( )
     return ( )
 endif ( )
diff --git a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS64.cmake b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS64.cmake
index 744aaef91..1a5c63690 100644
--- a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS64.cmake
+++ b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS64.cmake
@@ -37,7 +37,7 @@ set ( SuiteSparse_BLAS_integer "int64_t" )
 # https://github.com/spack/spack/blob/develop/var/spack/repos/builtin/packages/suite-sparse/package.py
 
 if ( DEFINED BLAS64_SUFFIX )
-    # append BLAS64_SUFFIX to each BLAS and LAPACK name
+    # append BLAS64_SUFFIX to each BLAS and LAPACK function name
     string ( FIND ${BLAS64_SUFFIX} "_" HAS_UNDERSCORE )
     message ( STATUS "BLAS64_suffix: ${BLAS64_SUFFIX}" )
     if ( HAS_UNDERSCORE EQUAL -1 )