diff --git a/CMakeLists.txt b/CMakeLists.txt
index 757b45e5..dd3c4322 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -666,6 +666,11 @@ if (ENABLE_TRILINOS)
       set( TRILINOS_CXX_COMPILER ${CMAKE_CURRENT_BINARY_DIR}/trilinos/src/trilinos/packages/kokkos/bin/nvcc_wrapper )
     endif()
 
+    set( TRILINOS_ENABLE_SERIAL ON )
+    if( ENABLE_OPENMP OR ENABLE_CUDA )
+      set( TRILINOS_ENABLE_SERIAL OFF )
+    endif()
+
     ExternalProject_Add( trilinos
                          PREFIX ${PROJECT_BINARY_DIR}/trilinos
                          URL ${TRILINOS_URL}
@@ -721,7 +726,7 @@ if (ENABLE_TRILINOS)
                                     -D KOKKOS_ENABLE_CUDA_LAMBDA:BOOL=${ENABLE_CUDA}
                                     -D KOKKOS_ENABLE_CUDA_UVM:BOOL=${ENABLE_CUDA}
                                     -D Tpetra_ENABLE_CUDA:BOOL=${ENABLE_CUDA}
-                                    -D Tpetra_INST_SERIAL:BOOL=ON
+                                    -D Tpetra_INST_SERIAL:BOOL=${TRILINOS_ENABLE_SERIAL}
                                     -D Tpetra_INST_INT_LONG_LONG:BOOL=ON
                                     -D Tpetra_INST_INT_INT:BOOL=OFF
                                     -D Tpetra_INST_DOUBLE:BOOL=ON
@@ -729,6 +734,7 @@ if (ENABLE_TRILINOS)
                                     -D Belos_ENABLE_Tpetra:BOOL=ON
                                     -D Belos_ENABLE_Epetra:BOOL=OFF
                                     -D Belos_ENABLE_Xpetra:BOOL=OFF
+                                    -D Ifpack2_ENABLE_ThyraTpetraAdapters:BOOL=OFF
                                     ${TRILINOS_EXTRA_ARGS}
                         )