By M.P. MCQUEEN

The housing crash has left at least 11 million people in the unenviable position of owing more on their homes than they are worth—and many more millions with properties worth far less than they paid for them.

But some might not be as trapped as they think. Record-low mortgage rates and a new slump in home prices are presenting unusual opportunities in the housing market these days—even for so-called underwater borrowers.

Some intrepid homeowners are intentionally taking a loss on their current house—and writing a big check to retire their old mortgage—in order to buy twice the home for not much more money. Others, eschewing conventional personal-finance advice, are even opting for “cash-in” refinancings, paying thousands of dollars out of pocket to settle old loans—and then taking out new mortgages with lower payments, shorter durations or both.

Katie Everett, a real-estate broker in Denver, says none of her clients kicked in cash when selling their homes last year. This year, “about half are willing to bring money to closing, anywhere from $5,000 to $45,000,” she says.

Are these people crazy to be tying up even more of their cash in their homes, in effect doubling down on what has been a losing bet thus far? After all, any number of variables, from the employment picture to the credit markets, could weigh on housing for years to come.

Yet economists say trading up to new homes or refinancing existing ones can be smart—even if it means plunking down more cash to get out of old mortgages. People living in less-desirable neighborhoods might be able to find better homes in tonier ones that offer better appreciation potential. And with mortgage rates so low, such buyers can keep their monthly payments manageable, even though the new homes are more expensive.

“If you are trading up, what better time than when interest rates are at record lows and the cost of the trade-up is much less than it used to be?” says Christopher J. Mayer, a Columbia Business School economist.

The refinancing equation is changing, too. Thanks to rock-bottom interest rates and liberal lending terms for Federal Housing Administration loans, a person who plunks down cash to retire a higher-rate mortgage might be able to reduce his monthly payments, even as he shortens his loan term to 20, 15 or 10 years.

In the past, financial planners typically recommended that homeowners devote as little cash to real estate as possible, and to invest it in the financial markets instead. But with stocks essentially where they were 11 years ago and market volatility seemingly on the rise, people are rethinking that wisdom. Devoting extra cash to repay a mortgage early is among the safest ways to produce an investment return.

“At this point,” says Jay Brinkmann, chief economist of the Mortgage Bankers Association in Washington, “if they don’t have anything else that is bringing a tremendous return, then they are buying themselves an annuity by paying their house off sooner than they needed to.”

During the fourth quarter of 2009, 33% of refinancings were of the cash-in variety, the highest percentage since Freddie Mac began tracking the characteristics of refinance transactions in 1985. Figures for the second quarter are due next week.

“Historically high percentages of borrowers are paying down their principal when they refinance their mortgages,” says Brad German, a Freddie Mac spokesman.

It helps that interest rates are lower than they have been in decades. The average rate on a 30-year fixed-rate loan was about 4.74% on July 21, according to Bankrate.com. That is down from 5.26% in January. Rates on 15-year loans averaged about 4.18%.

The Mortgage Bankers Association said Wednesday that low interest rates sent the volume of mortgage applications 7.6% higher during the week ended July 16. Purchase applications increased for just the second time since the expiration of a temporary federal tax break in May. Refinance applications grew 8.6%, to the highest level since May 2009.

The attractive terms are spurring people like Scott Ayler, 35 years old, into action. He and his wife, Jaclyn, 33, recently decided to trade up to a larger home in their native Denver, despite taking a loss on their current house. In 2004, they paid $234,000 for a three-bedroom, 2½-bath house builtthat same year in Green Valley Ranch, a subdivision that has among the highest foreclosure rates in the city and lacks upscale amenities. They are in contract to sell the home for about $204,000.

Their new home, built this year, cost about $323,000, comes with four bedrooms and three baths, and sits on a corner lot overlooking a reservoir. The house, which was initially listed at $379,000, is in Denver’s desirable Cherry Creek area, known for excellent schools, plentiful amenities and few foreclosures.

With $195,000 remaining on their original 6.625%, 30-year fixed-rate loan, the Aylers estimate their total paper loss will be around $45,000. They are putting down only $11,500 on the new house. But because the new FHA loan carries a 4.5% rate, their monthly payment will rise by only $290 a month.

They say they expect better price appreciation in their new home. And with a young daughter and plans for another child, they need more space anyway.

“We don’t want to wait for the market to come back,” says Mr. Ayler, general counsel for an energy company. “We wanted a better quality of life now.”

Of course, many homeowners in states like Arizona, Florida and Michigan are seriously underwater, having overpaid for houses now worth as little as half their value at the market’s peak. Making up that yawning gap and scraping up additional cash for a new down payment is beyond their means.

Some of those people are going to extremes by engaging in “strategic defaults,” a highly controversial strategy in which they stop paying their mortgages and go into foreclosure to get out of their obligations. But while cutting losses on a bad housing investment might seem liberating, it can stain a person’s credit report for years.

The vast majority of homeowners remain reluctant to sell their primary residence at a loss, perhaps irrationally so. In a study of seller behavior in condominium transactions in downtown Boston from 1990 to 1997, economists David Genesove of Hebrew University in Jerusalem and Prof. Mayer of Columbia showed that sellers were so “averse to nominal losses” that it affected their behavior. Those who were selling their homes in down markets and faced the possibility of nominal losses kept their homes on the market for much longer than other sellers, in some cases to their detriment.

“Loss aversion is a very, very strong force,” Prof. Mayer says. “People don’t like to sell their homes for less than they paid for it.”

But, he adds: “Why should it matter? If you sell a home for less than you pay for it, you would buy for less, too.”

Others are coming around to that view. In Minneapolis, real-estate agent Jason Walgrave says he recently helped a couple buy a 2,800 square-foot home in nearby Plymouth, Minn., an affluent suburb, for $325,000. To get there, they sold for $175,000 a 1,500 square-foot house for which they had paid $190,000 in 2005. Their existing home is financed with a 7.5% mortgage; they will get 4.5% on the new one.

The couple is bringing $25,000 to the closing table to pay off the old loan and closing costs. “They want to take advantage of the bigger house at a lower price and the lower interest rate,” Mr. Walgrave says. Now, for an extra $390 a month, they are getting almost twice as much house.

Just as old beliefs about selling houses are being upended, the conventional wisdom surrounding refinancing is changing, too. Time was when the only question about a refinance deal was how much money the homeowner could take out of the house. From the 1980s through the mid-2000s, the so-called cash-out refi became an easy way for homeowners to spend beyond their means.

Now, some homeowners are doing the opposite: writing big checks to pay off their old mortgages and taking out new ones with far lower interest rates, shorter repayment terms or both.