TRACON Controller described a confused altitude assignment event involving a military flight. The reporter commenting on the excessive speeds of the military aircraft adding to the complication.

Narrative

Busy session; numerous over flights requiring course changes to avoid traffic. Six or seven arrivals to different airports descending through over flights and several departures. A satellite prop arrival was coming in from the North at 10000 and an over flight was off the departure end; NE bound at 11000. Two F16's departed routed N climbing to 15000. A military intercept was squawking 7777. I assumed this was in error and I informed the lead. I turned the aircraft to 020 heading to split the other traffic and allow the climb to continue. I consciously thought about re-assigning the altitude but after the squawk thing; the turn and traffic issuance; I didn't want to throw any more numbers at the pilot who would increase the transmissions and potential confusion. I wanted to get this guy on course and off my frequency but had to wait until he topped the guy at 10000. Made numerous other transmissions then looked at the F16's and he was climbing very fast as I was about to transmit. The F16's showed 16000 and asked if they were cleared to the block. I said no; assigned altitude 15000 contact ZKC. No traffic observed; but at 560 KTS; aircraft can mess things up pretty quick.