diff --git a/tools/pybind11Config.cmake.in b/tools/pybind11Config.cmake.in
index 9808f3d25..9921aeb35 100644
--- a/tools/pybind11Config.cmake.in
+++ b/tools/pybind11Config.cmake.in
@@ -87,7 +87,7 @@ you can either use the basic targets, or use the FindPython tools:
   target_link_libraries(MyModule2 pybind11::headers)
   set_target_properties(MyModule2 PROPERTIES
                                   INTERPROCEDURAL_OPTIMIZATION ON
-                                  CXX__VISIBILITY_PRESET ON
+                                  CXX_VISIBILITY_PRESET ON
                                   VISIBLITY_INLINES_HIDDEN ON)
 
 If you build targets yourself, you may be interested in stripping the output
diff --git a/tools/pybind11NewTools.cmake b/tools/pybind11NewTools.cmake
index 686450bc3..96879d3ce 100644
--- a/tools/pybind11NewTools.cmake
+++ b/tools/pybind11NewTools.cmake
@@ -214,8 +214,18 @@ function(pybind11_add_module target_name)
     target_link_libraries(${target_name} PRIVATE pybind11::python2_no_register)
   endif()
 
-  set_target_properties(${target_name} PROPERTIES CXX_VISIBILITY_PRESET "hidden"
-                                                  CUDA_VISIBILITY_PRESET "hidden")
+  # -fvisibility=hidden is required to allow multiple modules compiled against
+  # different pybind versions to work properly, and for some features (e.g.
+  # py::module_local).  We force it on everything inside the `pybind11`
+  # namespace; also turning it on for a pybind module compilation here avoids
+  # potential warnings or issues from having mixed hidden/non-hidden types.
+  if(NOT DEFINED CMAKE_CXX_VISIBILITY_PRESET)
+    set_target_properties(${target_name} PROPERTIES CXX_VISIBILITY_PRESET "hidden")
+  endif()
+
+  if(NOT DEFINED CMAKE_CUDA_VISIBILITY_PRESET)
+    set_target_properties(${target_name} PROPERTIES CUDA_VISIBILITY_PRESET "hidden")
+  endif()
 
   # If we don't pass a WITH_SOABI or WITHOUT_SOABI, use our own default handling of extensions
   if("${type}" STREQUAL "MODULE" AND (NOT ARG_WITHOUT_SOABI OR NOT "WITH_SOABI" IN_LIST
diff --git a/tools/pybind11Tools.cmake b/tools/pybind11Tools.cmake
index aee60db28..3fa452f97 100644
--- a/tools/pybind11Tools.cmake
+++ b/tools/pybind11Tools.cmake
@@ -174,8 +174,13 @@ function(pybind11_add_module target_name)
   # py::module_local).  We force it on everything inside the `pybind11`
   # namespace; also turning it on for a pybind module compilation here avoids
   # potential warnings or issues from having mixed hidden/non-hidden types.
-  set_target_properties(${target_name} PROPERTIES CXX_VISIBILITY_PRESET "hidden"
-                                                  CUDA_VISIBILITY_PRESET "hidden")
+  if(NOT DEFINED CMAKE_CXX_VISIBILITY_PRESET)
+    set_target_properties(${target_name} PROPERTIES CXX_VISIBILITY_PRESET "hidden")
+  endif()
+
+  if(NOT DEFINED CMAKE_CUDA_VISIBILITY_PRESET)
+    set_target_properties(${target_name} PROPERTIES CUDA_VISIBILITY_PRESET "hidden")
+  endif()
 
   if(ARG_NO_EXTRAS)
     return()