Braid can be a pain when jigging, but if you keep a little tension on the spool with your thumb as you lift & drop it works pretty good. The "rounder" braids like Power Pro and the new Stren (haven't tried the Stren yet) don't dig into the spool as much as the flatter braids do. I feel your pain about losing nice fish. 4 years ago I had some 65 lb Tuf Line loop around the rod tip and a slab darn near pulled me in the drink.
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It's wonderful to be good. But it's better if you're lucky and good!