The CEO of Southwest Airlines says June revenue looks weaker than May, and he doesn’t yet see signs of a turnaround.

“It’s a very, very difficult time, and earnings are going to be very stressed until the economy changes,” Gary Kelly says.

Revenue divided by capacity, a key measurement in the airline business, was weaker in June than in May, according to Kelly, although he didn’t give any figures.

The Dallas-based airline is responding by cutting unprofitable flights, adding fees for unaccompanied minors and pets, and offering incentives for employees to leave the airline.

Copyright 2009 The Associated Press.