Originally Posted by FBinNY

A bit of perspective here. We're talking about realigning the wheel off an "old Schwinn Varsity", certainly not something built to raceworthy standards. The reason I said the tire needs to come off is that it's probably a single wall rim and not knowing the history a diligent mechanic would remove the tire to make sure that his work doesn't bring spokes too high and puncture the tube, which was a common problem in that era.

It's also easier to work on these types of wheels with the tire off because it's easier to detect the rocking (not hop or wobble but twist in the rim) that happens these Endrich pattern rims.