I usually will not go to a smaller fly, more or less because I don't want to decrease the average size of fish I'm catching. When I keep getting short strikes, I borrow a page from saltwater and do a very slow hand-over-hand retrieve. When I feel a take, I just continue to retrieve the fly until there's pressure moving in the opposite direction. That's when a fish has truly taken the fly, and that's when I do an additional strip set.
It can be hard not to set the hook when you feel the taps of smaller fish, especially when you can see them coming. As weird as this may sound, don't be afraid to do the hand-over-hand retrieve with your eyes closed or looking away once you see fish headed towards the fly. Rely on feel, and you'll get more fish.