iTunes & Genius Mixes

Does anyone know of a way to influence the Dozen "Mixes" that iTunes creates, I have ripped all of my music even some of the stuff I dont play much any more if at all, is there a way to influence the mixes you get offered to focus in on the stuff I want to play more.

Turning off Genius then Un-ticking everything I'm not too interested in then turning it on again sort of improved the mixes but I don't know if that was just coincidence and they would have changed anyway.