Just recently I've learnt that I like to add gritty and mean distortion to a sound where I use heavy sidechained compression to make it as mean as possible, since it's ducking so heavy you don't pay that much attention to how destroyed the sound actually may be.
Another thing is to use a pre-tone if you do more real distortion than warm and cozy saturation.
One pre-tone trick is to add an EQ before a heavy distortion, do a major boost on the lowend, like 40-60 Hz, depending what frequency suits the best, then after the distortion you just highpass that lowend away, and now the sound is gritty as if there were some kind of amplitude modulation going on (sounds great on claps!). You can also do this inside a synth sound that features much distortion - just add a sub oscillator that is just booming, then highpass it away after the distortion. I do this a lot when I sounddesign.