Partially addresses #16360

Change-Id: Ic098d2c465742fb50aee325a3fd0e1d50b7b3c99
Reviewed-on: https://go-review.googlesource.com/25575Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>