Redo of CL 28575 with fixed test.
We're in a pre-KeepAlive world for a bit yet, the old tests
were in a client which was in a post-KeepAlive world.

Change-Id: I114fd630339d761ab3306d1d99718d3cb973678d
Reviewed-on: https://go-review.googlesource.com/28582
Run-TryBot: Keith Randall <khr@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>