Rates for full-time vs. part-time projects

I'm working as a freelance software developer. I have a full-time (40 hour/week) project, but I have talked to a couple companies about picking up some part-time work in addition. If the rate I'm getting paid for the full-time is $X/hour, should I be shooting for $X on part-time work? Is it reasonable for clients to expect to pay a bit less, since they'll have less of my focus?