(FORTUNE Magazine) – As the summer travel season approaches, the once shadowy business of discount overseas air travel is coming out into the sunshine. Amazing deals are available (see table), great news for vacationers. But if you're thinking of cutting your corporate travel bill with these fares, think twice. U.S. regulations and international agreements between governments and airlines are supposed to prohibit deep discounting, but it has flourished anyway because of simple economics. As Pan Am executive Edward Mehler points out, empty airplane space is ''like overripe fruit in the supermarket -- if you don't move it, it becomes worthless.'' So airlines anticipating empty seats on a flight quietly sell blocks of them at considerable discounts to broker-dealers called consolidators and to certain travel agencies. Discounting started as mainly a mom-and-pop business concentrating on ethnic markets, but some operators are becoming big time. One of the fastest growing is Access International, which sold $14 million of tickets to the public last year. Based in New York, it has opened offices in Paris and recently in London. Venerable Thomas Cook Ltd., owned by Britain's Midland Bank, has set up its own consolidator, Airfare Warehouse Ltd., which supplies Cook's 400 retail branches with tickets discounted up to 50%. U.S. corporate travelers are not flocking to the low fares. One reason: A ) ticket sold by a discounter will not be honored by airlines other than the one for which it was issued. It is usually not refundable, and it may carry other restrictions. In addition, while many discount tickets are for flights on established Western carriers, some put travelers on unfamiliar Third World lines. Airfare Warehouse's lowest scheduled New York-London round-trip coach fare in May was $360, available only on Third World carriers such as Kuwait Airways. Standard coach fare on a major carrier is $1,462. Vacationers may find discount fares to Europe harder to get this summer as foreign travel recovers from last year's slump and airlines are able to sell more seats at full fares. Paris could be the divine exception, blessed with overcapacity as American and Continental join Air France, Pan Am, and TWA in daily service from New York.

CHART: YOU CAN GET THERE FOR A LOWER FARE

ONE WAY STANDARD GRAY FROM . . . TO COACH MARKET

New York London $731 $200 New York Paris $648 $210 Chicago Rome $855 $300 Chicago Tokyo $995 $579 Los Angeles Tokyo $705 $499 Los Angeles Hong Kong $832 $449

CREDIT: ILLUSTRATION BY SUSAN PIZZO CAPTION: YOU CAN GET THERE FOR A LOWER FARE DESCRIPTION: Standard coach and gray market airline fares for several routes.