A Controller at ZME reported an aircraft needed emergency descent from FL380. He separated traffic to the extent possible to clear the descent path using non standard procedures.

Narrative

Air Carrier X was enroute at FL380. The pilot advised me that they wanted to start down to FL320 for a pressurization problem. I had two aircraft which I had just taken the hand off on climbing to FL340. Air Carrier Y was right under Air Carrier X and Aircraft Z just in front of him. I cleared Air Carrier X to FL350 and issued the Air Carrier Y traffic right under him. Air Carrier X then asked for lower; in the high twenties; [so] I re-cleared him to maintain FL350 and issued the traffic on Aircraft Z. At this point I asked if this was an emergency. He said it could be. I then turned Aircraft Z to the east to make sure the targets didn't merge and issued Air Carrier X a heading to maintain. Aircraft Z reported Air Carrier X in sight and that they were clear. Around this time Air Carrier X said he needed to keep coming down. I said roger; issued the traffic and told him to maintain FL350 unless this is an emergency. He said it was now an emergency. I told him to maintain FL240 so he wouldn't violate the lower stratum if he needed to continue down. After Air Carrier X got lower and the situation improved for him I asked him if FL260 would work for him. He requested FL280 for now. I re-cleared him to maintain FL280. This was an emergency situation. Aircraft Z had Air Carrier X in sight and said that they were clear of him. [The] targets weren't going to merge and I felt this was a dire enough situation that Air Carrier X needed to descend immediately or else the situation could get far worse. In the future I would probably not issue an altitude to the aircraft to maintain in case he needed to continue down for emergency reasons.