diff --git a/Lib/trace.py b/Lib/trace.py
index db36e1d..35edac2 100644
--- a/Lib/trace.py
+++ b/Lib/trace.py
@@ -179,9 +179,11 @@
     # looking in sys.path for the longest matching prefix.  We'll
     # assume that the rest is the package name.
 
+    comparepath = os.path.normcase(path)
     longest = ""
     for dir in sys.path:
-        if path.startswith(dir) and path[len(dir)] == os.path.sep:
+        dir = os.path.normcase(dir)
+        if comparepath.startswith(dir) and comparepath[len(dir)] == os.sep:
             if len(dir) > len(longest):
                 longest = dir
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 06dde4a..7e94560 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -64,6 +64,9 @@
 Library
 -------
 
+- Patch #1536071: trace.py should now find the full module name of a
+  file correctly even on Windows.
+
 - logging's atexit hook now runs even if the rest of the module has
   already been cleaned up.