ejvc on another site suggests using honeycomb stitch (if your sewing machine has this) instead of a coverstitch. I have tried it, and it works on a medium weight jersey ok, but is less successful on a lighter weight.
I have a Bernina combo overlocker/coverstitch and it is a PIG to alter. I think I did it once successfully. 

I sometimes cut a square (say 5cm by 5cm), pour boiling water on it, squeeze it in a towel then iron it dry. Then I check for shrinkage and change of how it handles. (Not advisable for synthetics!). I mostly use natural fabrics, linens and cottons, and in the summer will wash the whole lot first (after overlocking).  This takes out (most!) of the shrinkage.

Hi, has anyone else got once of these machines? What have you made on it? I bought one about 18 months ago, refused to listen to the dealer when he tried to demo it in my home, and spent months trying to rethread it. I eventually watched an online tutorial and realised that if I had listened I would have understood that it only looks like conventional threading but is certainly not. I haven't thought of a freehand project yet (Wabi Sabi style) but will probably start with a shopping bag as my old ones I made are beginning to wear out.
My local Oxfam shop has a craft corner that does a roaring trade - sells donated bits of cloth and threads and other habbie stuff. One person's reject is definitely another one's treasure !