diff --git a/setup.py b/setup.py
index 545143a..eab1f59 100644
--- a/setup.py
+++ b/setup.py
@@ -527,8 +527,11 @@
         # The _tkinter module.
         
         # Assume we haven't found any of the libraries or include files
+        # The versions with dots are used on Unix, and the versions without
+        # dots on Windows, for detection by cygwin.
         tcllib = tklib = tcl_includes = tk_includes = None
-        for version in ['8.4', '8.3', '8.2', '8.1', '8.0']:
+        for version in ['8.4', '84', '8.3', '83', '8.2',
+                        '82', '8.1', '81', '8.0', '80']:
              tklib = self.compiler.find_library_file(lib_dirs,
                                                      'tk' + version )
              tcllib = self.compiler.find_library_file(lib_dirs,
@@ -586,8 +589,9 @@
         if platform in ['aix3', 'aix4']:
             libs.append('ld')
 
-        # Finally, link with the X11 libraries
-        libs.append('X11')
+        # Finally, link with the X11 libraries (not appropriate on cygwin)
+        if platform != "cygwin":
+            libs.append('X11')
 
         ext = Extension('_tkinter', ['_tkinter.c', 'tkappinit.c'],
                         define_macros=[('WITH_APPINIT', 1)] + defs,