If your compass does not work on all headings, when you factor in documented magnetic deviaton in the earth, or deviation in your compass, then the answer is to overhaul or replace it. Many pilots do tend to forget the magnetic dip lead/lag momentary heading distortions when turning from a heading of north (tends to lead the turn) or south (lags) depending on the rate of the turn...mostly because we've become spoiled by DGs and such.
The formula can get complicated - latitude, degree of bank and such - but generally overshooting a turn from or through a turn to the south by 30 degrees (unless you're honking that baby over), and undershooting by the same amount if you're turing from or past a heading of north, works out pretty well.
East and west courses have fewer distortions...unless you're accelerating or slowing down.
Of course, I may have it all backwards or sideways...I dunno. When first I flew my airplane had nothing so fancy as a DG, but that was a long time ago. Just look it up.
Oh, and as bizarre as this sounds, the law insists you have a compass deviation card attached to this ancient instrument or, technically at least, the aircraft is not legally airworthy. A few years back I swung my compass...oh what a PITA!
Jonathan