I have a sparrow problem as well... Last year was my first attempt with Purple Martins, in June a got 12 room S&K house with tri-tel pole and as soon as I put it up I had one male and two female Purple Martins, they started to build immediately (one above the other one). Half way through their building a male sparrow started to build a nest on the other side of the house. At that point I started to read about being a PM landlord on various websites/forums and decided to start taking out the nest daily while my trap that fits my house from PMCA arrives. The male sparrow would build a new nest within a few hours every morning. Finally the trap came in and it worked great I caught a pair, because by that time he already had a female. After that... four more sparrows showed up and started building, when I would trapping in one compartment they would build in the other, I would pull those nests and then the worst happen they moved to the other side and took over both of my Purple Martin nests. Both of my females left, one sooner than the other, but my male hang around for awhile, he would come in the mornings and try to attract other females the would fly by.
That's when I decided to get a Blain's repeating trap and build Brad Biddles trap myself, between those two I caught up to 12 sparrows every day and in total last fall I trapped 148 sparrows. You would think that put a dent in their presence in my neighborhood, not a chance... the moment I've put up my s&k housing this year, one male and two females showed up the following day and started building their nest. Since Martins are not back, I got two of them with mouse glue...
The one good thing this year is that they have not showed an interest in my deluxe gourd rack that I have purchased last year, but I don't know what will happen when PM arrive...
So what I'm trying to say here

that if your are able get many different types of traps... I'm also not good shooter at the live targets, so far I was able to nip a starling, but I've yet to hit a sparrow...