We have a larson trap, if we start having a problem I bait it with eggs, catches the actual offenders, then hopefully more.
We also have a friendly 'local' gamekeeper (some distance but only one around), I've let him set a big trap and it's caught lots of the crow family this year, he left us another larson trap and we've had 8.
I'm also thinking of the songbirds, one year there was a goldfinch nest, i saw the magpie there, later the nest was wrecked. Very sad.