Fixes #4943
Fixes #4687
Fixes #7079

Change-Id: Ia96f07d650a3af935cd75fd7e3253f4af2977429
Reviewed-on: https://go-review.googlesource.com/7890Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>