After English sparrows take over my bluebird box, I deploy an old rat trap....

IM NOT SURE but that system can whack good song birds also. There is a trap that fits inside birdhouse and when tripped puts a orange set off in hole inside house. You put a big laundry bag over whole house. Open door if male or female sparrow...uthanize it.... no hurt on bluebird or good songbird. Google BRAW... has info on traps and bluebird house plans.
Blue Bird Restoration Association of Wisconsin.

Sparrow lives matter!

These traps are fairly inexpensive, and attached to the inside of the house. Very effective.
I build 4 boxes specifically for these traps and run them around my yard in early spring to thin out the house sparrows before the Purple Martins show up.
Once wrens, tree swallows and bluebirds show up I pull the traps to prevent accidental catches, and wait till sparrows are using the house before reinstalling, usually catch the offenders in 10-15 minutes, then remove trap and clean out box.

https://vanerttraps.com/shop/ols/products/universal-sparrow-trap

Never whack the bluebirds, or tree swallows. Bluebirds never approach a box with active sparrows. Been busting sparrows this way for a few years now.

Tried the other live catch in-box method and had some sparrows escape when I tried to grab then in my net, before I could grab them with my hands.

Nope

Invasive

I take out the sparrows with my pellet gun. Can't get any more selective than that.

Dang britts. Them starlings are bad here too. And quite slick.
410 w/#8's on the wing. Fun too !
wrens sometimes go where mice do. Snagged a few eatin peanut butter outa mouse traps on the porch in behind and under the furniture. I hated that, love the wrens.

If wrens were the size of a robin, there would be no housecats.

Ha .. probably right. Like a flying shrew.
I guess we have the House Wren here. Some have longer tails than others. I've watched them fill all of my houses to the brim with sticks, just so no other bird can use them.
Jammed full and sticking out of the hole.
My favorite little loud mouth. If they were big as a crow, there wouldn't be a window unbroken.