People are flying again ... sort of

After weeks of essentially zero demand for US air travel, even a small improvement in passenger demand, bookings, and trip cancellations, is a step in the right direction. Southwest said the number of flight bookings outpaced cancellations over the past month. Cancellations had been outpacing bookings during the majority of March and April.

The picture still isn't rosy: Southwest expects its revenue to be down between 85% to 90% in May compared to a year ago. Southwest predicts it will sell only 25% to 30% of the seats on its greatly reduced schedule of flights this month. As bad as that is, it's better than its earlier forecast of a 90% to 95% drop in revenue, when Southwest expected to sell just 5% to 10% of its flights.

It hasn't changed its guidance for how many flights it expects to have this month, and Southwest still forecasts that the schedule will reduced by 60% to 70% from last year's schedule for the month.

But Southwest raised its forecast for June: It said it expects to have only a 45% to 55% reduction in capacity in the month. And it expects June revenue to be down 80% to 85T, selling only 30% to 45% of seats.

Still, the company cautioned that the environment remains uncertain.

Southwest is the nation's fourth largest airline behind American, Delta and United, said its final numbers for April show revenue down between 90% to 95%, and that it sold only 8% of its seats.

Southwest CEO Gary Kelly has repeatedly said that he expected air travel would start to return when the country started to reopen. But he said he didn't know how much, and how fast, that return in demand would take place.

JetBlue Airways also told investors on a recent call that it believes the low point in air travel demand was reached in mid-April, although its executives also warned the recovery would be slow.