It will take some digging and maybe a bit of luck to score a cheap airfare for this summer.

So far airlines are withholding their deepest discounts from prime summer travel periods, although they have been offering sales for domestic and international flights this spring — even some astounding bargains.

Take Tuesday, for example.

Without much fanfare, Delta Air Lines offered flights this spring to some European cities for as little as $138 round trip. Taxes included. The offer was gone within a few hours, leading some experts to think it was a pricing error. Delta declined to comment.

"These are massive, massive sales, and this is the third time we've seen this since late last year," said George Hobica, founder of travel-advice website airfarewatchdog.com. He said Delta and Lufthansa have each offered cut-rate fares in recent months.

The sudden and temporary nature of the deepest sales makes it harder for travelers to find them. In one instance Hobica says Lufthansa mistakenly priced flights without fuel surcharges, and the lower prices lasted only until the German carrier fixed the error, which wasn't long.

Other sales are easier to spot. They often run from Tuesdays through Thursdays. This week, Southwest Airlines put many U.S. destinations on sale for as low as $138 round trip, with blackout days around Easter and on Fridays and Sundays. Other airlines matched the prices.

To find the most deals, experts like Hobica and Tom Parsons of BestFares.com advise travelers to sign up for airline loyalty programs and alerts from travel websites, and to follow the same sources on Twitter.

Airlines constantly advertise sales, but so far the deals have been limited to travel before late May. Parsons says travelers should look for one airline to break free from the pack and extend a sale into summer.

"When they do, you better be ready with your credit card, because that first sale usually delivers more bang for the buck," he says.

Rick Seaney, CEO of FareCompare.com, says base fares are poised to rise as much as $250 per round trip because airlines aren't yet discounting summer seats. He says prices might come down as airlines unload unsold inventory, but they could also go higher.

Seaney says we're approaching the time — about three months before summer vacations begin — when airlines traditionally start offering bargains to gauge travel demand.

Jet fuel prices could be the wild card. Fuel and labor are an airline's two biggest costs, and fuel prices have risen nearly 50 percent in the past year, as oil prices have climbed. The Air Transport Association, an industry group, estimates that every dollar increase in the price of oil costs U.S. airlines an extra $400 million per year.

Air fares rose last summer as demand for travel increased and airlines tightly controlled the number of flights and seats. Last June, average fares were 18 percent higher than the summer before, although increases were more modest after that. Airlines are continuing to add surcharges of $20 to $60 per round trip on peak travel days, including spring break, holidays and summer.

Many flights last summer took off with 90 percent or more of the seats filled, and the Federal Aviation Administration forecasts that even more people will travel in 2011 than last year.

The FAA predicts that passengers on U.S. airlines will pay 2 percent more for domestic flights and 5 percent more for international trips this year.