'IT'S the best deal right now - believe me!"The United Airlines agent in New York City's crowded midtown ticket office was trying to explain to a bewildered customer just why buying a round trip New York-Chicago ticket 14 days in advance was actually $100 less than the usually cheaper 21-day advance fare. The reason was competition: a special promotional fare to spur slow winter traffic. The logic behind some discount air fares continues to elude many customers. But that's not stopping them. Price-conscious travelers are giving the airlines a run for their money. Though air passenger traffic is expected to be down 2 percent this year, a growing share of those who are flying - some 95 percent - now ferret out some kind of discount fare. The restrictions - advance purchase, little or no money back if plans change, a Saturday night stayover - often grate. Yet most flyers would rather put up with them than pay more. Many ticket buyers say they now persist until they are sure they have been told the lowest possible fares. m not nearly as interested in the date I travel as the rate I pay," says one Washington, D.C., woman. "We find that about half of our advance ticket buyers are not only willing but quite able to take advantage of the [deepest] 21-day discount," notes American Airlines spokesman Tim Smith, who says it is typically about one-third of the full coach fare. "Leisure travelers are booking further and further out." The prod to fly discount, for most passengers, is a combination of the recession and what they see as outlandish regular coach fares. Technically, such fares remained flat this year. Yet few passengers are willing to pay the standard round trip New York-Chicago fare of $838, a price that a few years ago took Chicagoans to Europe and back, or the round trip $500 fare between Boston and Washington. "When I hear one of those really wacko prices, I say, 'Gee, the airlines must not want people to fly very muc h, says one Bostonian. United Airlines spokeswoman Lynn Martenstein says a new interest among business travelers in taking advantage of the seven-day advance purchase fare is a key reason for recent discount fare growth. One New York professional who flies frequently to the Midwest says he buys his nonrefundable tickets well in advance. When his plans change, he says he can sometimes convince airline employees that filling an empty seat makes more sense economically than following rules to the letter. "I say, 'You inconvenience me when you cancel or delay flights - I have a right to change my plans too. The question of whether to fill empty seats by charging below-cost prices or keep prices at cost, leaving more seats empty, is a constant challenge for airlines. Experts say that newly refined software can closely track such rapidly changing prices and seat inventories, making frequent checks by travel agents and passengers worthwhile. "It's very possible to call an airline in some cases and get a deal," says Dan Smith, a consumer spokesman for the Texas-based International Airline Passengers Association . Though Continental Airlines just this week began adding $20 round trip on a number of discount fares, a move followed by other major airlines, most experts say discount fares are here to stay. "They've become a way of life," says Lee Howard, president of Airline Economics Inc. To help spur more people to fly during the slow winter months ahead, most US airlines are offering sharp discounts of almost 50 percent on fares across the Atlantic. Round trip flights from Boston are running as low as $318. Yet Mr. Howard, who points out that the airlines will end this year with at least a $1.8 billion operating loss on top of last year's $2.4 billion, says that the industry is also long overdue for some "catch-up" in average fares.