Get a good bait trap and use white millet seed for bait and you won't have to shoot many. I use to sell House Sparrow traps on the Internet, but that was a few years ago. Just google House Sparrow bait traps. I think there is one called "uncle Blaines sparrow trap." I caught over 300 in the first 6 months of trapping that I did. I have Purple Martins and Bluebirds and they are very bothersome to them. They'll kill Bluebirds, and poke holes in Martin eggs. I hate them. The bait traps don't work as well in the spring, but during mid summer through winter, you can't beat them.
I am having more problems with them this spring than usual. I have shot 11 of them in the past week. I use Aguilla Sniper Sub Sonic ammo. It's very, very accurate and quiet. I recheck my zero with every lot # change of that ammo that I shoot. I usually buy 3 or 4 boxes at a time and just had to buy some new ammo last week. My normal sparrow shot is 40 yards, so that's where I keep that rifle zeroed. With the new ammo I shot two 3 shot groups at 40 yards. The first 3 shots were 1/4 inch left, adjusted the scope, then the next 3 shots were dead center. You could cover both groups at the same time with a penny I guess.