diff --git a/Modules/FindPythonLibs.cmake b/Modules/FindPythonLibs.cmake
index 0749efcfb..27d9e4503 100644
--- a/Modules/FindPythonLibs.cmake
+++ b/Modules/FindPythonLibs.cmake
@@ -80,10 +80,15 @@ endif()
 
 # Set up the versions we know about, in the order we will search. Always add
 # the user supplied additional versions to the front.
-set(_Python_VERSIONS
-  ${Python_ADDITIONAL_VERSIONS}
-  ${_PYTHON_FIND_OTHER_VERSIONS}
-  )
+# If FindPythonInterp has already found the major and minor version,
+# insert that version between the user supplied versions and the stock
+# version list.
+find_package(PythonInterp QUIET)
+set(_Python_VERSIONS ${Python_ADDITIONAL_VERSIONS})
+if(DEFINED PYTHON_VERSION_MAJOR AND DEFINED PYTHON_VERSION_MINOR)
+  list(APPEND _Python_VERSIONS ${PYTHON_VERSION_MAJOR}.${PYTHON_VERSION_MINOR})
+endif()
+list(APPEND _Python_VERSIONS ${_PYTHON_FIND_OTHER_VERSIONS})
 
 unset(_PYTHON_FIND_OTHER_VERSIONS)
 unset(_PYTHON1_VERSIONS)