diff --git a/perf_test/sparse/KokkosSparse_spmv_struct_tuning.cpp b/perf_test/sparse/KokkosSparse_spmv_struct_tuning.cpp
index 02fcd1640a..85aab62122 100644
--- a/perf_test/sparse/KokkosSparse_spmv_struct_tuning.cpp
+++ b/perf_test/sparse/KokkosSparse_spmv_struct_tuning.cpp
@@ -581,7 +581,9 @@ int main(int argc, char** argv) {
       const double alpha = 1.0, beta = 1.0;
       size_t bufferSize = 0;
       void* dBuffer     = NULL;
-#if CUSPARSE_VERSION >= 11201
+
+// CUSPARSE_MM_ALG_DEFAULT was deprecated in CUDA 11.2.1 a.k.a cuSPARSE 11.4.0
+#if CUSPARSE_VERSION >= 11400
       cusparseSpMVAlg_t alg = CUSPARSE_SPMV_ALG_DEFAULT;
 #else
       cusparseSpMVAlg_t alg = CUSPARSE_MV_ALG_DEFAULT;
diff --git a/sparse/tpls/KokkosSparse_spmv_tpl_spec_decl.hpp b/sparse/tpls/KokkosSparse_spmv_tpl_spec_decl.hpp
index 23d85c0b5c..6ac5f49296 100644
--- a/sparse/tpls/KokkosSparse_spmv_tpl_spec_decl.hpp
+++ b/sparse/tpls/KokkosSparse_spmv_tpl_spec_decl.hpp
@@ -65,6 +65,8 @@ void spmv_cusparse(const Kokkos::Cuda& exec,
       !Kokkos::ArithTraits<value_type>::isComplex)
     myCusparseOperation = CUSPARSE_OPERATION_TRANSPOSE;
 
+// Hopefully this corresponds to CUDA reelase 10.1, which is the first to
+// include the "generic" API
 #if defined(CUSPARSE_VERSION) && (10300 <= CUSPARSE_VERSION)
 
   using entry_type = typename AMatrix::non_const_ordinal_type;
@@ -105,7 +107,7 @@ void spmv_cusparse(const Kokkos::Cuda& exec,
 
   size_t bufferSize = 0;
   void* dBuffer     = NULL;
-#if CUSPARSE_VERSION >= 11301
+#if CUSPARSE_VERSION >= 11400
   cusparseSpMVAlg_t alg = CUSPARSE_SPMV_ALG_DEFAULT;
 #else
   cusparseSpMVAlg_t alg = CUSPARSE_MV_ALG_DEFAULT;
@@ -113,13 +115,13 @@ void spmv_cusparse(const Kokkos::Cuda& exec,
   if (controls.isParameter("algorithm")) {
     const std::string algName = controls.getParameter("algorithm");
     if (algName == "default")
-#if CUSPARSE_VERSION >= 11301
+#if CUSPARSE_VERSION >= 11400
       alg = CUSPARSE_SPMV_ALG_DEFAULT;
 #else
       alg = CUSPARSE_MV_ALG_DEFAULT;
 #endif
     else if (algName == "merge")
-#if CUSPARSE_VERSION >= 11301
+#if CUSPARSE_VERSION >= 11400
       alg = CUSPARSE_SPMV_CSR_ALG2;
 #else
       alg = CUSPARSE_CSRMV_ALG2;