This is Quentin's https://golang.org/cl/33012 with updated tests.

Fixes #14186

Change-Id: Ib51deaab0368c6bad32ce9d6345119ff44f3c2d6
Reviewed-on: https://go-review.googlesource.com/33291Reviewed-by: Quentin Smith <quentin@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>