How To Get Rid of Mice That Don't Trigger Traps? -- Good Questions

Q: We live in an inner-city apartment. While it's a great old building, we've got a mouse problem. We've talked to building maintenance, they put out traps and bait. We've put out traps and bait. We've caught a total of two mice in traps and caught another two by cornering them and catching them in a plastic cup.