I have a Channel Master CM3039. It definitely makes a difference (I lost the signal, completely, without the amp) but I still get drop-outs. Usually one every few minutes, and more on UHF. What would you suggest that might do a little better job than this one?

You might need a better antenna to feed a better signal to the amp in the first place - the amp can only amplify what it's given.

Think of it as a funnel under a waterfall in a small stream. If use a funnel with a 6-inch mouth, you will capture much more water than with a funnel with a 2-inch mouth. If you put a pump on the output of the 2-inch funnel, the water will be shoved out from the funnel faster, but you still won't get as much water as with the 6-inch funnel.

I understand all of that but I'd still like to try a better amplifier before I get a bigger antenna as I don't really have a place for a much bigger antenna than I have.

Unless you have a very long cable run or are splitting the signal many times, most of the common amplifiers have about the same effect on SNR at the receiver. More gain will have almost no improvement on this value and at the point where the amp overloads the SNR of many channels will be degraded a lot. That said the RESEARCH COMMUNICATIONS 9260 amp may get a 2-3 dB improvement on UHF channels, if your antenna is not picking up too much noise. No preamp will help if your problem is from multipath, interferance or very deep signal fades due to cars, airplanes, or variable propagation.
John