How can I avoid gr clumps being left on the lawn after I mow?

I'm seeing lots of gr clippings left in my yard after I mow. I know some of the problem is that the gr is growing really fast and is very long when it is cut. Also, I have mowed when the gr isn't completely dry. Short of buying a new mower, is there any other way to avoid these leftover clumps in the lawn?