i have a ehx black finger, dual tube compressor, and use it extensively... even too much!
it's not an overdrive, of course, but it gives my cleans a dirtier tone that i love (i set it on quite obtrusive compression levels)... dynamics are of course sacrificed, even if on high gain levels it becomes unapparent. if you use often cleans/slight overdrive for soloing you should better switch it off, but i find it essential for rhythm.
it's the first thing in the pre-chain, just after the guitar.