Removes another per-request allocation. Also makes the code more
readable, IMO. And more testable.

benchmark                                   old ns/op    new ns/op    delta
BenchmarkServerFakeConnWithKeepAliveLite        10539        10324   -2.04%

benchmark                                  old allocs   new allocs    delta
BenchmarkServerFakeConnWithKeepAliveLite           20           19   -5.00%

benchmark                                   old bytes    new bytes    delta
BenchmarkServerFakeConnWithKeepAliveLite         1609         1559   -3.11%

R=golang-dev, gri
CC=golang-dev
https://golang.org/cl/8118044