Some don't use the offside hand at all and as little contact as possible with the trigger hand, I prefer to hold the wrist loosely with my trigger hand and put a finger over the top of the barrel just ahead of the scope with just enough pressure to keep it on the rest but allow it to slide back at recoil, sort of a modified free recoil.
With light recoiling varmint calibers I don't use my offside hand at all. The more body contact with high power scopes causes heart beat movement of the rifle and can be seen in the scope which isn't conducive to great accuracy.
Tim