Good suggestion, but it didn't solve the problem. LimeWire was already running at Normal priority. I tried setting it to the two lower settings, and it still caused other applications to slow down and still took greater than 85% of the CPU. The stuttering of music playing from iTunes decreased though. It didn't stop, but it did get less frequent.

Just for grins I tried setting it to priority High. Boy was that a mistake! Took me 5 minutes to kill LimeWire since even the Task Manager wouldn't respond anymore.