Bought an 86 Bianchi Sport SX this past week as a commuter bike. I live in Alabama, but found the bike on CL out in LA. I had a friend out there meet the seller, and take delivery of the bike. I paid DTLA to do an overhaul service, and to pack and ship the bike to me.

Nevertheless, the brake calipers are a problem at the moment. One pad on each of the calipers is rubbing the rim when the brake is disengaged. The calipers seem centered, and I have even attempted tightening them off-center to compensate away from the rubbing pad. However, when I tighten the brake for the first time after adjustment, the brake goes back to rubbing. Any ideas on how I can fix this? I am fairly handy with mechanical work...I have just never done my own bike repairs. So any advice would be welcome.

Brakes are Dia Compe (caliper says 400 on the back of one arm and 5M88432 on the other.