diff --git a/var/spack/repos/builtin/packages/geant4/CLHEP-10.03.03.patch b/var/spack/repos/builtin/packages/geant4/CLHEP-10.03.03.patch
new file mode 100644
index 0000000000..b865f3bde2
--- /dev/null
+++ b/var/spack/repos/builtin/packages/geant4/CLHEP-10.03.03.patch
@@ -0,0 +1,34 @@
+diff --git a/cmake/Modules/FindCLHEP.cmake b/cmake/Modules/FindCLHEP.cmake
+index 8b59f1c0a..f616d678e 100644
+--- a/cmake/Modules/FindCLHEP.cmake
++++ b/cmake/Modules/FindCLHEP.cmake
+@@ -180,7 +180,10 @@ if(UNIX)
+         execute_process(COMMAND ${CLHEP_CONFIG_EXECUTABLE} --prefix
+             OUTPUT_VARIABLE _clhep_config_prefix
+             OUTPUT_STRIP_TRAILING_WHITESPACE)
+-
++          if (_clhep_config_prefix)
++            # Remove wrapping double quotes.
++            string(REGEX REPLACE "\"(.*)\"" "\\1" _clhep_config_prefix "${_clhep_config_prefix}")
++          endif()
+         list(APPEND _clhep_root_hints ${_clhep_config_prefix})
+     endif()
+ elseif(WIN32 AND NOT UNIX)
+diff --git a/cmake/Templates/Geant4Config.cmake.in b/cmake/Templates/Geant4Config.cmake.in
+index d6fe408b3..f355be2af 100644
+--- a/cmake/Templates/Geant4Config.cmake.in
++++ b/cmake/Templates/Geant4Config.cmake.in
+@@ -268,13 +268,7 @@ set(Geant4_builtin_clhep_FOUND @GEANT4_USE_BUILTIN_CLHEP@)
+ if(NOT Geant4_builtin_clhep_FOUND)
+   set(Geant4_system_clhep_ISGRANULAR @GEANT4_USE_SYSTEM_CLHEP_GRANULAR@)
+ 
+-  set(CLHEP_ROOT_DIR "@CLHEP_ROOT_DIR@")
+-  set(__GEANT4_OLD_CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH})
+-  set(CMAKE_MODULE_PATH "${_geant4_thisdir}/Modules" ${CMAKE_MODULE_PATH})
+   find_package(CLHEP @CLHEP_VERSION@ REQUIRED @__g4_clhep_components@)
+-  set(CMAKE_MODULE_PATH ${__GEANT4_OLD_CMAKE_MODULE_PATH})
+-  unset(CLHEP_ROOT_DIR)
+-  unset(__GEANT4_OLD_CMAKE_MODULE_PATH)
+   #CLHEP doesn't use target properties fully yet, so always include_directories
+   include_directories(${CLHEP_INCLUDE_DIRS})
+ endif()
diff --git a/var/spack/repos/builtin/packages/geant4/package.py b/var/spack/repos/builtin/packages/geant4/package.py
index 085a5dc604..f2934817df 100644
--- a/var/spack/repos/builtin/packages/geant4/package.py
+++ b/var/spack/repos/builtin/packages/geant4/package.py
@@ -38,22 +38,19 @@ class Geant4(CMakePackage):
 
     # C++11 support
     depends_on("xerces-c cxxstd=11", when="cxxstd=11")
-    depends_on("clhep@2.4.0.0 cxxstd=11", when="@10.04 cxxstd=11")
-    depends_on("clhep@2.3.4.6 cxxstd=11", when="@10.03.p03 cxxstd=11")
+    depends_on("clhep@2.3.3.0: cxxstd=11", when="@10.03.p03: cxxstd=11")
     depends_on("vecgeom cxxstd=11", when="+vecgeom cxxstd=11")
 
     # C++14 support
     depends_on("xerces-c cxxstd=14", when="cxxstd=14")
-    depends_on("clhep@2.4.0.0 cxxstd=14", when="@10.04 cxxstd=14")
-    depends_on("clhep@2.3.4.6 cxxstd=14", when="@10.03.p03 cxxstd=14")
+    depends_on("clhep@2.3.3.0: cxxstd=14", when="@10.03.p03: cxxstd=14")
     depends_on("vecgeom cxxstd=14", when="+vecgeom cxxstd=14")
 
     # C++17 support
     depends_on("xerces-c cxxstd=17", when="cxxstd=17")
+    depends_on("clhep@2.3.3.0: cxxstd=17", when="@10.03.p03: cxxstd=17")
     patch('cxx17.patch', when='@:10.03.p99 cxxstd=17')
     patch('cxx17_geant4_10_0.patch', level=1, when='@10.04.00: cxxstd=17')
-    depends_on("clhep@2.4.0.0 cxxstd=17", when="@10.04 cxxstd=17")
-    depends_on("clhep@2.3.4.6 cxxstd=17", when="@10.03.p03 cxxstd=17")
     depends_on("vecgeom cxxstd=17", when="+vecgeom cxxstd=17")
 
     depends_on("expat")
@@ -74,12 +71,17 @@ class Geant4(CMakePackage):
     depends_on('geant4-data@10.03.p03', when='@10.03.p03 ~data')
     depends_on('geant4-data@10.04', when='@10.04 ~data')
 
+    # As released, 10.03.03 has issues with respect to using external
+    # CLHEP.
+    patch('CLHEP-10.03.03.patch', level=1, when='@10.03.p03')
+
     def cmake_args(self):
         spec = self.spec
 
         options = [
             '-DGEANT4_USE_GDML=ON',
             '-DGEANT4_USE_SYSTEM_CLHEP=ON',
+            '-DGEANT4_USE_SYSTEM_CLHEP_GRANULAR=ON',
             '-DGEANT4_USE_G3TOG4=ON',
             '-DGEANT4_INSTALL_DATA=ON',
             '-DGEANT4_BUILD_TLS_MODEL=global-dynamic',