The painful sting attached to many non-refundable airline tickets has been all but eliminated in the new domestic-fare structures announced in the past week and a half by most major U.S. airlines.

Along with lower fares, the easing of the non-refundable rules should be a welcome boon.Designed to simplify the nation's complex fare system, the new arrangement seems nevertheless to have confused some travelers and even airline reservation clerks.

Basically, the move has substantially cut the cost of first-class and unrestricted coach fares most frequently used by business travelers; trimmed most leisure fares, although not by as much; and made it easier for leisure travelers to change lower-priced non-refundable tickets.

As of last week, American, which introduced the changes, had been followed by United, Delta, Northwest, USAir and Continental in adopting the system. So far TWA has not joined and probably won't.

The new structure provides for four basic fare categories: first class, unrestricted coach, seven-day advance purchase (non-refundable) and 21-day advance purchase (non-refundable). But some airlines have variations.

In all the hoopla over lower fares, the easing of restrictions on non-refundable tickets seems to have been overlooked. But there has been a very basic change in these tickets, making them much more flexible to use.

Until last week, passengers purchasing a non-refundable ticket tended to be locked into their trip. If they wanted to cancel or change their departure or return dates, they faced penalties that ranged up to a full 100 percent of the ticket cost. Most of these restrictions have been abolished.

Now travelers taking advantage of non-refundable tickets' cheaper fares can change tickets with relative ease for just $25, a nominal administrative fee. For this fee, entirely new departure and return dates can be booked, which comes in handy if a trip must be postponed.

But in addition, and this is a big plus, travelers can apply the value of their unused ticket toward a new ticket. If they so choose, they can go to an entirely different destination.

As an example, take the case of a couple who books a non-refundable ticket to San Francisco to attend a convention. At the last minute they can't make the trip and have no reason to fly to San Francisco at a later date. They can't get a refund, but they do get full credit (less the $25 fee) for the price they paid for tickets to an alternate destination of their choice.

The only stipulations, as American Airlines spells out in its rules, is that the traveler must meet the applicable advance-purchase and length-of-stay requirements for the new destination. The non-refundable tickets still require a Saturday-night stay and must be purchased within 24 hours of making a reservation.

American anticipates that by lowering the penalty to $25, the airline will eliminate the hassle faced by some passengers of getting a doctor's note if they became ill and canceled a non-refundable ticket, according to spokeswoman Lise Olson. Paying the $25 fee to change dates or itinerary might be simpler for most travelers.

In introducing its new four-tier fare structure on April 9, American eliminated a variety of ticket categories, including such advance-purchase options as 14-day and 30-day tickets. However, TWA is still offering 14-day and 30-day fares - some of them cheaper than the 21-day tickets other airlines are selling - and USAir has retained some 14-day fares in markets in which it competes directly with TWA.

On the surface, at least, most of the new fares appear to be cheaper than those previously available. American said it was cutting its first-class fares by 20 to 50 percent and its unrestricted coach fares by 38 percent, and United announced it was trimming its seven-day advance-purchase fares by 30 percent and its 21-day fares by 20 percent.

As early as last Monday, many travelers who had already bought tickets at higher fares were turning them in for refunds on the difference between the old and new fares. I got a $39 refund on an already discounted $438 round-trip ticket between Washington and San Francisco I had purchased earlier.

American planned its new fare structure months in advance, and its competition is scrambling to catch up. As a result, some reservation clerks remained uncertain last week as to what the new rules did or did not permit.

Most of the airlines have been announcing their new policies in full-page ads in daily newspapers. For a while, it could be helpful to clip them as a way to compare.