diff --git a/git_map.py b/git_map.py
index f93e6b896..700132516 100755
--- a/git_map.py
+++ b/git_map.py
@@ -1,4 +1,8 @@
 #!/usr/bin/env python
+# Copyright 2014 The Chromium Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+
 """
 Provides an augmented `git log --graph` view. In particular, it also annotates
 commits with branches + tags that point to them. Items are colorized as follows:
diff --git a/git_map_branches.py b/git_map_branches.py
index 5fde84b28..fc6c8cec4 100755
--- a/git_map_branches.py
+++ b/git_map_branches.py
@@ -1,4 +1,8 @@
 #!/usr/bin/env python
+# Copyright 2014 The Chromium Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+
 """
 Provides a short mapping of all the branches in your local repo, organized by
 their upstream ('tracking branch') layout. Example:
@@ -45,7 +49,14 @@ def print_branch(cur, cur_hash, branch, branch_hashes, par_map, branch_map,
   else:
     color += Style.NORMAL
 
-  print color + "  "*depth + branch + (" *" if branch == cur else "")
+  suffix = ''
+  if cur == 'HEAD':
+    if branch_hash == cur_hash:
+      suffix = ' *'
+  elif branch == cur:
+    suffix = ' *'
+
+  print color + "  "*depth + branch + suffix
   for child in par_map.pop(branch, ()):
     print_branch(cur, cur_hash, child, branch_hashes, par_map, branch_map,
                  depth=depth+1)
diff --git a/git_nav_downstream.py b/git_nav_downstream.py
index 9c2a53780..e394343ba 100755
--- a/git_nav_downstream.py
+++ b/git_nav_downstream.py
@@ -1,4 +1,8 @@
 #!/usr/bin/env python
+# Copyright 2014 The Chromium Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+
 """
 Checks out a downstream branch from the currently checked out branch. If there
 is more than one downstream branch, then this script will prompt you to select
@@ -14,7 +18,11 @@ def main(argv):
   upfn = upstream
   cur = current_branch()
   if cur == 'HEAD':
-    upfn = lambda b: hash_one(upstream(b))
+    def _upfn(b):
+      parent = upstream(b)
+      if parent:
+        return hash_one(parent)
+    upfn = _upfn
     cur = hash_one(cur)
   downstreams = [b for b in branches() if upfn(b) == cur]
   if not downstreams: