Partially addresses #16360

Change-Id: I67a328302d7d91231f348d934e4232fcb844830a
Reviewed-on: https://go-review.googlesource.com/27398Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>