(MONEY Magazine) – Do you find the arithmetic behind auto leasing a bit hard to grasp? Apparently some banks have had the same problem. So many lost money in the auto leasing business last year that you may now have to pay more to lease your favorite car, minivan or sport utility.

I happen to prefer buying to leasing because owning a car gives me the freedom to decide when it's time for a new one. But if you're among the one in three new-car shoppers who favors leasing, you may be surprised the next time you trade in for a new lease. "People are turning in cars after two to three years of paying $300 a month," says David McKay, an auto finance specialist at J.D. Power & Associates. "Now they hear that lease payments for the same model will be $400." Take the popular Jeep Grand Cherokee Laredo. Last year, many Chrysler dealers were pushing $269-a-month, 36-month leases on the Jeep; this year you'll have to pay $359 a month for the same lease.

To understand what's happening, you need a little industry background. Traditionally, the best lease deals come from the "captive" finance subsidiaries of the automakers, such as General Motors Acceptance Corp. In the early to mid-1990s, most captives bet that used-car prices would rise more quickly than expected, which let them aggressively cut lease costs. (Lease payments cover the difference between the price of the car, or capitalized cost, and the residual value at the end of the lease, plus interest.) When the value of the used cars being turned in from leases rose by 6% to 9% a year, the captives covered their bet.

But when banks such as Wells Fargo, Chase and Bank One copied that strategy in 1995 and 1996, the market didn't bail them out. In 1997 and 1998 used-car prices flattened and then declined, leaving banks with two- and three-year-old cars they couldn't sell for enough to cover their investment. The Consumer Bankers Association estimates that banks have lost money on about three-quarters of leases in the past few years--with shortfalls averaging $1,800 per car. One notable casualty, Bank One, lost $102 million on leasing in 1998.

This year, chastened banks are setting lower, more realistic residual values on new leases--and charging higher payments as a result. Captive-finance companies, whose losses were less severe, are also retrenching, limiting low payments to models they especially want to promote, according to Michael Scott Kranitz, author of Look Before You Lease and president of the www.leasesource.com website. Great lease deals do remain--just don't expect them to be as widespread as they once were. Here's how to get one:

UNEARTH PROMOTIONS. When car makers, lenders and dealers want to push a model, they can cut lease payments one of three ways: inflate the residual value, cut the capitalized cost or charge a low interest rate (or "money factor"). In the table above, I've listed four current lease deals that sport one or more of these cost breaks. If none of these vehicles suit you, try to negotiate for one of these breaks in any deal you're offered. To see how the residual value compares with the industry norm, go to www.carwizard.com. There you'll find the Automotive Lease Guide (ALG) estimate of what your car will be worth at the end of the lease term, expressed as a percentage of the price. If the residual value is two percentage points or more above the ALG value--a less common occurrence nowadays--you're being offered a promotional lease.

To figure out if the capitalized cost has been cut, look up the dealer's invoice cost at the same site. You're getting a favorable deal if the capitalized cost is no more than $500 over the dealer's invoice (including options). The money factor--which you should try to get below 5%--appears in dense-looking decimals such as 0.001430. Don't be daunted. Multiply that figure by 2400 for an approximate annual interest rate (3.4% in this case).

HIRE HELP. These changes in the lease climate may be reason enough to consult an expert. I find that these services can usually save you money, even after their fees. CarSource (800-517-2277) will track down the best lease deal in your area and close it for $475. If you just want assistance analyzing a specific deal, a service rep at Chart Software's leasing hotline (800-418-8450) will help you develop a counteroffer for $35 per lease.

Profit from their losses. If you want to buy the car that you're leasing now, these industry woes could work in your favor. An inflated residual value may mean that your lease's buy-out price is higher than your car's current value (which you can look up at www.edmunds.com). If so, call the bank or finance company and offer the market value, which many lenders will accept--or bargain from--to avoid having to take a loss.