This procedure for unclogging a toilet worked for me. It involves pouring in hot water and dish soap. It seems risky, but there have been no apparent problems. After pouring in the hot water it might be good to wait half an hour or so before flushing, to avoid the stress of a sudden temperature change.
Well, one problem: putting the plunger in the hot water caused the rubber cup to shrink and distort, so the plunger is now useless.