Rich, I think every situation is different - line test, river currents, snags, obstacles to a following pursuit, etc. In general I lean toward putting the most pressure possible that fit the conditions; despite the consensus fish fight harder when fought harder. But sometimes a little finess can be a better way to go. One example is when a fish wants to take a long run, allow it to do so without trying to stop or even significantly impead it because letting it run further with just moderate drag on it will tire it out faster, unless the conditions demand stopping it (such as keeping it away from a fight ending snag or heading right for a swift tailout/rapids when you can't follow it). Sometimes keeping the rod tip very low to the water or evening down into the water can help turn a fish around when heading toward trouble. So can a sudden free spool of slack line to get a line belly drag from below the fish to make it run back into the hole away from the downstream drag (a last resort - and hope the hook is set deeply). Also during the fight keep trying to turn it's head toward you. One way I do both that and tire them faster is to put a quick but smooth harder line tug with your rod when the head shake is coming toward you, while just holding the rod steady when the headshake is going away from you. This seems to often turn the fish your way to help keep the fight in closer where you can play it more aggressively. And know your line's limits well! Then just keep after it without making any serious mistakes. The rest is usually up to the luck factor when playing a trophy fish in a tough place.

RT