diff --git a/core/src/Cuda/Kokkos_Cuda_Parallel.hpp b/core/src/Cuda/Kokkos_Cuda_Parallel.hpp
index 2ae1cc0dddf..3b0f9ad531b 100644
--- a/core/src/Cuda/Kokkos_Cuda_Parallel.hpp
+++ b/core/src/Cuda/Kokkos_Cuda_Parallel.hpp
@@ -525,6 +525,7 @@ class ParallelFor< FunctorType
   inline
   void execute() const
   {
+    if(m_rp.m_num_tiles==0) return;
     const array_index_type maxblocks = static_cast<array_index_type>(Kokkos::Impl::CudaTraits::UpperBoundGridCount);
     if ( RP::rank == 2 )
     {
diff --git a/core/unit_test/TestMDRange.hpp b/core/unit_test/TestMDRange.hpp
index 88b3a9b0c6e..a382a207002 100644
--- a/core/unit_test/TestMDRange.hpp
+++ b/core/unit_test/TestMDRange.hpp
@@ -956,7 +956,12 @@ struct TestMDRange_3D {
           }
         , Kokkos::Min<double>(min) );
 
-      ASSERT_EQ( min, 8.0 );
+      if((N0-1)*(N1-1)*(N2-1)>0)
+        ASSERT_EQ( min, 8.0 );
+      else {
+        double min_identity = Kokkos::reduction_identity<double>::min();
+        ASSERT_EQ( min, min_identity );
+      }
     }
 #endif
 #endif
diff --git a/core/unit_test/TestMDRange_d.hpp b/core/unit_test/TestMDRange_d.hpp
index 1a477a228fb..e25213a2893 100644
--- a/core/unit_test/TestMDRange_d.hpp
+++ b/core/unit_test/TestMDRange_d.hpp
@@ -46,8 +46,10 @@
 namespace Test {
 
 TEST_F( TEST_CATEGORY , mdrange_3d) {
+  TestMDRange_3D< TEST_EXECSPACE >::test_for3( 1, 10, 100 );
   TestMDRange_3D< TEST_EXECSPACE >::test_for3( 100, 10, 100 );
 #if !defined( KOKKOS_ENABLE_ROCM ) // MDRange Reduced explicitly handled in its own cpp file
+  TestMDRange_3D< TEST_EXECSPACE >::test_reduce3( 1, 10, 100 );
   TestMDRange_3D< TEST_EXECSPACE >::test_reduce3( 100, 10, 100 );
 #endif
 }
diff --git a/core/unit_test/TestViewCopy.hpp b/core/unit_test/TestViewCopy.hpp
index 7eab9daa11e..4771593228c 100644
--- a/core/unit_test/TestViewCopy.hpp
+++ b/core/unit_test/TestViewCopy.hpp
@@ -56,17 +56,13 @@ struct TestViewCopy {
 
   using InExecSpace = ExecSpace;
 
-  static void test_view_copy()
+  static void test_view_copy(const int dim0, const int dim1, const int dim2)
   {
 #if defined( KOKKOS_ENABLE_CUDA ) || defined( KOKKOS_ENABLE_ROCM )
    // ExecSpace = CudaUVM, CudaHostPinned
    // This test will fail at runtime with an illegal memory access if something goes wrong
    // Test 1: deep_copy from host_mirror_space to ExecSpace and ExecSpace back to host_mirror_space
    {
-    const int dim0 = 4;
-    const int dim1 = 2;
-    const int dim2 = 3;
-
     typedef Kokkos::View<double****,InExecSpace> Rank4ViewType;
     Rank4ViewType view_4;
     view_4 = Rank4ViewType("view_4", dim0, dim1, dim2, dim2);
@@ -88,10 +84,6 @@ struct TestViewCopy {
 
    // Test 2: deep_copy from Cuda to ExecSpace and ExecSpace back to Cuda
    {
-    const int dim0 = 4;
-    const int dim1 = 2;
-    const int dim2 = 3;
-
     typedef Kokkos::View<double****,InExecSpace> Rank4ViewType;
     Rank4ViewType view_4;
     view_4 = Rank4ViewType("view_4", dim0, dim1, dim2, dim2);
@@ -118,10 +110,6 @@ struct TestViewCopy {
 
    // Test 3: deep_copy from host_space to ExecSpace and ExecSpace back to host_space
    {
-    const int dim0 = 4;
-    const int dim1 = 2;
-    const int dim2 = 3;
-
     typedef Kokkos::View<double****,InExecSpace> Rank4ViewType;
     Rank4ViewType view_4;
     view_4 = Rank4ViewType("view_4", dim0, dim1, dim2, dim2);
@@ -149,7 +137,8 @@ struct TestViewCopy {
 
 TEST_F( TEST_CATEGORY , view_copy_tests ) {
   //Only include this file to be compiled with CudaUVM and CudaHostPinned
-  TestViewCopy< TEST_EXECSPACE >::test_view_copy();
+  TestViewCopy< TEST_EXECSPACE >::test_view_copy(4,2,3);
+  TestViewCopy< TEST_EXECSPACE >::test_view_copy(4,2,0);
 }
 
 } // namespace Test