diff --git a/include/openmc/mesh.h b/include/openmc/mesh.h
index 44b1aa8c3..5d9b2f5a6 100644
--- a/include/openmc/mesh.h
+++ b/include/openmc/mesh.h
@@ -397,6 +397,7 @@ public:
 private:
   moab::Range ehs_; //!< Range of tetrahedra EntityHandle's in the mesh
   moab::EntityHandle meshset_; //!< EntitySet containing all Tets/Tris
+  moab::EntityHandle tet_set_;
   moab::EntityHandle kdtree_root_; //!< Root of the MOAB KDTree
   std::shared_ptr<moab::Interface> mbi_; //!< MOAB instance
   std::unique_ptr<moab::AdaptiveKDTree> kdtree_; //!< MOAB KDTree instance
diff --git a/src/mesh.cpp b/src/mesh.cpp
index 49eff192a..b74435a95 100644
--- a/src/mesh.cpp
+++ b/src/mesh.cpp
@@ -1583,6 +1583,17 @@ UnstructuredMesh::UnstructuredMesh(pugi::xml_node node) : Mesh(node) {
     warning("Non-tetrahedral elements found in unstructured mesh: " + filename_);
   }
 
+  // make an entity set for all tetrahedra (used later in output)
+  rval = mbi_->create_meshset(moab::MESHSET_SET, tet_set_);
+  if (rval != moab::MB_SUCCESS) {
+    fatal_error("Failed to create an entity set for the tetrahedral elements");
+  }
+
+  rval = mbi_->add_entities(tet_set_, ehs_);
+  if (rval != moab::MB_SUCCESS) {
+    fatal_error("Failed to add tetrahedra to an entity set.");
+  }
+
   compute_barycentric_data(ehs_);
   build_kdtree(ehs_);
 }
@@ -2118,8 +2129,12 @@ UnstructuredMesh::write(std::string base_filename) const {
   // add extension to the base name
   base_filename += ".h5m";
 
+  // write the tetrahedral elements of the mesh only
+  // to avoid clutter from zero-value data on other
+  // elements during visualization
+
   moab::ErrorCode rval;
-  rval = mbi_->write_mesh(base_filename.c_str());
+  rval = mbi_->write_mesh(base_filename.c_str(), &tet_set_, 1);
   if (rval != moab::MB_SUCCESS) {
     std::stringstream msg;
     msg << "Failed to write unstructured mesh " << id_;
diff --git a/src/state_point.cpp b/src/state_point.cpp
index 465bab506..a39b6f297 100644
--- a/src/state_point.cpp
+++ b/src/state_point.cpp
@@ -717,6 +717,7 @@ void write_unstructured_mesh_results() {
                                                    tally->id_,
                                                    simulation::current_batch,
                                                    w);
+
           umesh->write(umesh_filename);
         }
       }