diff --git a/django/contrib/staticfiles/handlers.py b/django/contrib/staticfiles/handlers.py
index b51b7c8fd5..962b835fef 100644
--- a/django/contrib/staticfiles/handlers.py
+++ b/django/contrib/staticfiles/handlers.py
@@ -35,8 +35,7 @@ class StaticFilesHandler(WSGIHandler):
         * the host is provided as part of the base_url
         * the request's path isn't under the media path (or equal)
         """
-        return (self.base_url[2] != path and
-            path.startswith(self.base_url[2]) and not self.base_url[1])
+        return path.startswith(self.base_url[2]) and not self.base_url[1]
 
     def file_path(self, url):
         """
diff --git a/django/contrib/staticfiles/views.py b/django/contrib/staticfiles/views.py
index 5df1a3eced..1a9c166ad7 100644
--- a/django/contrib/staticfiles/views.py
+++ b/django/contrib/staticfiles/views.py
@@ -34,6 +34,8 @@ def serve(request, path, document_root=None, insecure=False, **kwargs):
     normalized_path = posixpath.normpath(urllib.unquote(path)).lstrip('/')
     absolute_path = finders.find(normalized_path)
     if not absolute_path:
+        if path.endswith('/') or path == '':
+            raise Http404("Directory indexes are not allowed here.")
         raise Http404("'%s' could not be found" % path)
     document_root, path = os.path.split(absolute_path)
     return static.serve(request, path, document_root=document_root, **kwargs)