Start with your kick. I've noticed that drummers tend to muffle kicks more for live situations than is neccisary in the studio. Try taking the muffling material out of the kick and listen to the tuning and tone of the kick. Now check your snare. See what happens when you hit the kick.
Some rattle is cool, even desired, but too much can be a drag.
This is caused by sympathetic resonance from the kick. Adjusting the snare tension is the first thing to check. Now try hitting the snare while dampening the the heads in the manner I described. Use this procedure to determine what needs to be done to correct any problems and to decide which steps to take by way of tuning. You'd be surprised how little it takes to tune out excessive rattle from the snares.