The big obvious question here (to me at least) is: Are you compressing these mics as you track? Compression is going to bring the "bleed" level up dramatically. If you are... try not compressing so much... or at all.
You are always going to have bleed. How much (excluding compression issues) varies dramatically based on some of the following:
1. Mic choices
2. Mic positioning
3. The placement of the individual drums/cymbals
4. The Drummer
5. The Drummer
6. The Drummer
7. Oh... and the drummer.
What generally will not matter much is... preamp gain... unless you are cranked to the point where you are getting distortion and that rarely sounds good.
The drummer has a LOT to do with this. A drummer with great technique will allow you to mic in traditional methods with very little bleed (relatively speaking for drums). A drummer with bad teqhnique (and unsual cymbal placement) can make your life a nightmare. These facts are why engineers have developed a lot of different methods over years.
You can get rid of bleed issues on the drum mics by using good noise gates (I don't recommend this during tracking but I know some who do). This will give the kit a tighter, more focused sound generally. I almost ALWAYS mute tom tracks (in the mix) except for when they are struck and leave gates out of it all together... I just do it in the arrange window.
If you want the full sound of the kit... you can leave those mics open and ungated as well. Phase is very important. Check your individual instruments with the overheads... especially kick and snare. Make adjustments as necessary. Move the mics, and try toggling the phase (on kick snare) and listen to the low end to see which way sounds more solid.
Anyway... welcome to the art of recording drums. You will always have bleed, and that is part of the charm. Don't get caught up in what each drum sounds like soloed... listen to the kit as a whole. Don't overcompress (or even compress at all) going in... and just go for a "big picture" that rocks your world.
jmtc...