(CNN) -- Perhaps no system is more mysterious to travelers than airfare pricing. One minute it seems fares are up, the next minute they're down -- only to take off again before you can blink (or book). It's more dizzying than Friday afternoon air traffic at O'Hare.

To get inside the system, we talked with one of the folks who has helped design it. Dr. Richard Larson, a professor at M.I.T. and former officer of the Institute for Operations Research and the Management Sciences, is an expert on revenue management -- the construction and study of models to maximize profit in service industries such as air travel. He has served as a technical consultant to American Airlines and the Sabre Group.

Here are his tips for getting a great airfare:

Timing, timing, timing. It's not just when you book your ticket, but what kind you book.

"It's a lottery thing," says Larson. "In my field of operations research, it's called an action-timing problem: Dynamically over time you are offered opportunities to make decisions and once you say 'yes,' you cannot go back."

So, while you want to book early to take advantage of lower fares, you don't want to lock yourself in, in case something better comes along. Larson advises booking early -- but choosing deeply discounted refundable seats.

"That way, you know what your 'bird in hand' is, then you can keep calling and maybe you will find a non-refundable one that's cheaper."

Non-refundable? Not really... So you bought that discounted, non-refundable ticket to Timbuktu, then two weeks later the fares plummeted? All is not lost. Larson says if you keep checking fares and see something a whole lot better, it's worth it to cancel your original ticket, pay the $50 or $75 penalty, and re-book at the cheaper fare.

Wrap it up: Package deals. "If you deal with the airlines ... or with a travel agent, you can often get packages (that is air, hotel, car rental and other deals), for a much lower price than if you assembled things à la carte."

Also, if you have six or eight people flying, you may be eligible for special group fares.

Avoid the business stampede. Business travelers flood airports on Mondays and Fridays, so it's harder to find bargains on those days. Larson advises flying Tuesday, Wednesday or Thursday, especially mid-day. "Mid-day is a non-productive time for business travelers, so (it's) usually much more available in terms of deep discounts," says Larson. And, of course, don't forget the price break for that Saturday night stay.

How to book efficiently. While Larson advocates using the Internet to book travel, he also has advice for those who use the phone: "If you call the airlines directly, the queues are horrendous, but (most) travel agencies now charge a fee because airlines have cut commissions. Sometimes I find it worth it to pay that fee."

Another advantage of using a travel agent instead of calling the airline directly: Choices. "Calling an agent is like calling a broker; they have access to many airlines and deeper discount fares."

Use your e-mail. "Some of the airlines like American Airlines have e-ticket announcements on Wednesday of each week. If you just want to get away and you don't care where you go ... or if you can be flexible about when you do it, there are great deals." You can also sign up for e-mail services that notify you when fares to your selected destinations change.

If at first you fail to find a bargain, call, call again. "They revise the fare structures every night," says Larson. "It's amazing the amount of fare recalculations they do."