Quote - Well, if you know the map is going to be stretched when you bend the arms down, why not compress it in that direction so when it stretches, it produces something the correct size.

That would work, but you'd do it the other way around. You would stretch the polys in UV space to the relative size they'll be when the arms are down. Larger polys in UV space means more texture on each poly.

Depending on your software, one way to do this is to morph the model to a relaxed pose (arms down) before you UV map it, then morph it back to the T-pose for rigging.