diff --git a/packages/muelu/src/Graph/MatrixTransformation/MueLu_CoalesceDropFactory_kokkos_def.hpp b/packages/muelu/src/Graph/MatrixTransformation/MueLu_CoalesceDropFactory_kokkos_def.hpp
index b28d2e832765..301e0dbf1c7b 100644
--- a/packages/muelu/src/Graph/MatrixTransformation/MueLu_CoalesceDropFactory_kokkos_def.hpp
+++ b/packages/muelu/src/Graph/MatrixTransformation/MueLu_CoalesceDropFactory_kokkos_def.hpp
@@ -217,6 +217,8 @@ std::tuple<GlobalOrdinal, typename MueLu::LWGraph_kokkos<LocalOrdinal, GlobalOrd
 
   const bool useRootStencil   = pL.get<bool>("filtered matrix: use root stencil");
   const bool useSpreadLumping = pL.get<bool>("filtered matrix: use spread lumping");
+
+  const Scalar filteringDirichletThreshold = as<SC>(pL.get<double>("filtered matrix: Dirichlet threshold"));
   TEUCHOS_ASSERT(!useRootStencil);
   TEUCHOS_ASSERT(!useSpreadLumping);
 
@@ -692,18 +694,18 @@ std::tuple<GlobalOrdinal, typename MueLu::LWGraph_kokkos<LocalOrdinal, GlobalOrd
 
     if (lumping) {
       if (reuseGraph) {
-        auto fillFunctor = MatrixConstruction::PointwiseFillReuseFunctor<local_matrix_type, local_graph_type, true>(lclA, results, lclFilteredA, lclGraph);
+        auto fillFunctor = MatrixConstruction::PointwiseFillReuseFunctor<local_matrix_type, local_graph_type, true>(lclA, results, lclFilteredA, lclGraph, filteringDirichletThreshold);
         Kokkos::parallel_for("MueLu::CoalesceDrop::Fill_lumped_reuse", range, fillFunctor);
       } else {
-        auto fillFunctor = MatrixConstruction::PointwiseFillNoReuseFunctor<local_matrix_type, true>(lclA, results, lclFilteredA);
+        auto fillFunctor = MatrixConstruction::PointwiseFillNoReuseFunctor<local_matrix_type, true>(lclA, results, lclFilteredA, filteringDirichletThreshold);
         Kokkos::parallel_for("MueLu::CoalesceDrop::Fill_lumped_noreuse", range, fillFunctor);
       }
     } else {
       if (reuseGraph) {
-        auto fillFunctor = MatrixConstruction::PointwiseFillReuseFunctor<local_matrix_type, local_graph_type, false>(lclA, results, lclFilteredA, lclGraph);
+        auto fillFunctor = MatrixConstruction::PointwiseFillReuseFunctor<local_matrix_type, local_graph_type, false>(lclA, results, lclFilteredA, lclGraph, filteringDirichletThreshold);
         Kokkos::parallel_for("MueLu::CoalesceDrop::Fill_unlumped_reuse", range, fillFunctor);
       } else {
-        auto fillFunctor = MatrixConstruction::PointwiseFillNoReuseFunctor<local_matrix_type, false>(lclA, results, lclFilteredA);
+        auto fillFunctor = MatrixConstruction::PointwiseFillNoReuseFunctor<local_matrix_type, false>(lclA, results, lclFilteredA, filteringDirichletThreshold);
         Kokkos::parallel_for("MueLu::CoalesceDrop::Fill_unlumped_noreuse", range, fillFunctor);
       }
     }
@@ -854,6 +856,9 @@ std::tuple<GlobalOrdinal, typename MueLu::LWGraph_kokkos<LocalOrdinal, GlobalOrd
 
   const bool useRootStencil   = pL.get<bool>("filtered matrix: use root stencil");
   const bool useSpreadLumping = pL.get<bool>("filtered matrix: use spread lumping");
+
+  const Scalar filteringDirichletThreshold = as<SC>(pL.get<double>("filtered matrix: Dirichlet threshold"));
+
   TEUCHOS_ASSERT(!useRootStencil);
   TEUCHOS_ASSERT(!useSpreadLumping);
 
@@ -1095,18 +1100,18 @@ std::tuple<GlobalOrdinal, typename MueLu::LWGraph_kokkos<LocalOrdinal, GlobalOrd
 
     if (lumping) {
       if (reuseGraph) {
-        auto fillFunctor = MatrixConstruction::VectorFillFunctor<local_matrix_type, true, true>(lclA, blkPartSize, colTranslation, results, lclFilteredA, lclGraph);
+        auto fillFunctor = MatrixConstruction::VectorFillFunctor<local_matrix_type, true, true>(lclA, blkPartSize, colTranslation, results, lclFilteredA, lclGraph, filteringDirichletThreshold);
         Kokkos::parallel_for("MueLu::CoalesceDrop::Fill_lumped_reuse", range, fillFunctor);
       } else {
-        auto fillFunctor = MatrixConstruction::VectorFillFunctor<local_matrix_type, true, false>(lclA, blkPartSize, colTranslation, results, lclFilteredA, lclGraph);
+        auto fillFunctor = MatrixConstruction::VectorFillFunctor<local_matrix_type, true, false>(lclA, blkPartSize, colTranslation, results, lclFilteredA, lclGraph, filteringDirichletThreshold);
         Kokkos::parallel_for("MueLu::CoalesceDrop::Fill_lumped_noreuse", range, fillFunctor);
       }
     } else {
       if (reuseGraph) {
-        auto fillFunctor = MatrixConstruction::VectorFillFunctor<local_matrix_type, false, true>(lclA, blkSize, colTranslation, results, lclFilteredA, lclGraph);
+        auto fillFunctor = MatrixConstruction::VectorFillFunctor<local_matrix_type, false, true>(lclA, blkSize, colTranslation, results, lclFilteredA, lclGraph, filteringDirichletThreshold);
         Kokkos::parallel_for("MueLu::CoalesceDrop::Fill_unlumped_reuse", range, fillFunctor);
       } else {
-        auto fillFunctor = MatrixConstruction::VectorFillFunctor<local_matrix_type, false, false>(lclA, blkSize, colTranslation, results, lclFilteredA, lclGraph);
+        auto fillFunctor = MatrixConstruction::VectorFillFunctor<local_matrix_type, false, false>(lclA, blkSize, colTranslation, results, lclFilteredA, lclGraph, filteringDirichletThreshold);
         Kokkos::parallel_for("MueLu::CoalesceDrop::Fill_unlumped_noreuse", range, fillFunctor);
       }
     }
diff --git a/packages/muelu/src/Graph/MatrixTransformation/MueLu_MatrixConstruction.hpp b/packages/muelu/src/Graph/MatrixTransformation/MueLu_MatrixConstruction.hpp
index 1a5f2729c72e..640e1a6973c4 100644
--- a/packages/muelu/src/Graph/MatrixTransformation/MueLu_MatrixConstruction.hpp
+++ b/packages/muelu/src/Graph/MatrixTransformation/MueLu_MatrixConstruction.hpp
@@ -255,14 +255,17 @@ class PointwiseFillReuseFunctor {
   results_view results;
   local_matrix_type filteredA;
   local_graph_type graph;
+  scalar_type dirichletThreshold;
   const scalar_type zero = ATS::zero();
+  const scalar_type one  = ATS::one();
 
  public:
-  PointwiseFillReuseFunctor(local_matrix_type& A_, results_view& results_, local_matrix_type& filteredA_, local_graph_type& graph_)
+  PointwiseFillReuseFunctor(local_matrix_type& A_, results_view& results_, local_matrix_type& filteredA_, local_graph_type& graph_, scalar_type dirichletThreshold_)
     : A(A_)
     , results(results_)
     , filteredA(filteredA_)
-    , graph(graph_) {}
+    , graph(graph_)
+    , dirichletThreshold(dirichletThreshold_) {}
 
   KOKKOS_INLINE_FUNCTION
   void operator()(const local_ordinal_type rlid) const {
@@ -300,6 +303,8 @@ class PointwiseFillReuseFunctor {
     }
     if constexpr (lumping) {
       rowFilteredA.value(diagOffset) += diagCorrection;
+      if ((dirichletThreshold >= 0.0) && (ATS::real(rowFilteredA.value(diagOffset)) <= dirichletThreshold))
+        rowFilteredA.value(diagOffset) = one;
     }
   }
 };
@@ -323,13 +328,16 @@ class PointwiseFillNoReuseFunctor {
   local_matrix_type A;
   results_view results;
   local_matrix_type filteredA;
+  scalar_type dirichletThreshold;
   const scalar_type zero = ATS::zero();
+  const scalar_type one  = ATS::one();
 
  public:
-  PointwiseFillNoReuseFunctor(local_matrix_type& A_, results_view& results_, local_matrix_type& filteredA_)
+  PointwiseFillNoReuseFunctor(local_matrix_type& A_, results_view& results_, local_matrix_type& filteredA_, scalar_type dirichletThreshold_)
     : A(A_)
     , results(results_)
-    , filteredA(filteredA_) {}
+    , filteredA(filteredA_)
+    , dirichletThreshold(dirichletThreshold_) {}
 
   KOKKOS_INLINE_FUNCTION
   void operator()(const local_ordinal_type rlid) const {
@@ -356,6 +364,8 @@ class PointwiseFillNoReuseFunctor {
     }
     if constexpr (lumping) {
       rowFilteredA.value(diagOffset) += diagCorrection;
+      if ((dirichletThreshold >= 0.0) && (ATS::real(rowFilteredA.value(diagOffset)) <= dirichletThreshold))
+        rowFilteredA.value(diagOffset) = one;
     }
   }
 };
@@ -727,16 +737,19 @@ class VectorFillFunctor {
   results_view results;
   local_matrix_type filteredA;
   local_graph_type graph;
+  scalar_type dirichletThreshold;
   const scalar_type zero = ATS::zero();
+  const scalar_type one  = ATS::one();
 
  public:
-  VectorFillFunctor(local_matrix_type& A_, local_ordinal_type blockSize_, block_indices_view_type ghosted_point_to_block_, results_view& results_, local_matrix_type& filteredA_, local_graph_type& graph_)
+  VectorFillFunctor(local_matrix_type& A_, local_ordinal_type blockSize_, block_indices_view_type ghosted_point_to_block_, results_view& results_, local_matrix_type& filteredA_, local_graph_type& graph_, scalar_type dirichletThreshold_)
     : A(A_)
     , blockSize(blockSize_)
     , ghosted_point_to_block(ghosted_point_to_block_)
     , results(results_)
     , filteredA(filteredA_)
-    , graph(graph_) {}
+    , graph(graph_)
+    , dirichletThreshold(dirichletThreshold_) {}
 
   KOKKOS_INLINE_FUNCTION
   void operator()(const local_ordinal_type brlid) const {
@@ -773,6 +786,8 @@ class VectorFillFunctor {
       }
       if constexpr (lumping) {
         rowFilteredA.value(diagOffset) += diagCorrection;
+        if ((dirichletThreshold >= 0.0) && (ATS::real(rowFilteredA.value(diagOffset)) <= dirichletThreshold))
+          rowFilteredA.value(diagOffset) = one;
       }
     }
 
diff --git a/packages/muelu/src/Interface/MueLu_ParameterListInterpreter_def.hpp b/packages/muelu/src/Interface/MueLu_ParameterListInterpreter_def.hpp
index 36146faa491a..643b92518838 100644
--- a/packages/muelu/src/Interface/MueLu_ParameterListInterpreter_def.hpp
+++ b/packages/muelu/src/Interface/MueLu_ParameterListInterpreter_def.hpp
@@ -1059,6 +1059,11 @@ void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
       MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use lumping", bool, dropParams);
       MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: reuse graph", bool, dropParams);
       MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: reuse eigenvalue", bool, dropParams);
+      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use root stencil", bool, dropParams);
+      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: Dirichlet threshold", double, dropParams);
+      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: use spread lumping", bool, dropParams);
+      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: spread lumping diag dom growth factor", double, dropParams);
+      MUELU_TEST_AND_SET_PARAM_2LIST(paramList, defaultList, "filtered matrix: spread lumping diag dom cap", double, dropParams);
     }
 
     if (!amalgFact.is_null())
@@ -1313,7 +1318,6 @@ void ParameterListInterpreter<Scalar, LocalOrdinal, GlobalOrdinal, Node>::
 
   // Matrix analysis
   if (MUELU_TEST_PARAM_2LIST(paramList, defaultList, "matrix: compute analysis", bool, true)) {
-
     RCP<Factory> matrixAnalysisFact = rcp(new MatrixAnalysisFactory());
 
     if (!RAP.is_null())