Tough question, and as with almost any question involving bluebirds around here, the answer also involves Celery Farm Marsh Warden Emeritus Stiles Thomas.
The bluebird box was built in 1950s from plans drawn up by Stiles, and it even had Stiles' "brand" on the side of it.
Inside was an instruction sheet explaining where and how to place the nesting box, along with this warning:
"DO NOT UNDER [ANY] CIRCUMSTANCES ALLOW ENGLISH SPARROWS TO NEST IN THE BLUEBIRD HOUSE.
"You'll have to use ingenuity to defeat them. If removing their nests doesn't work, plug up the entrance hole for a few days. Another successful method is to place house with bottom just three feet from the ground. English sparrows don't normally nest this close to the ground. Bluebirds do."
NOTE: Correct me if I am wrong, but I think Stiles was referring to the bottom of the bluebird box, and not any other kind of bottom.
Congrats to Barbara Dilger for coming up with a mostly correct answer.
(The box was on the ground, by he way, because it has never been used. There's a concern that some of the old boards made from manmade materials won't stand up well to the weather.)