If you're trying to unload an SUV or a large pickup in favor of a fuel-efficient sedan, the market has put you between the proverbial rock and a hard place.

Not only are trade-in values and sales prices for used, fuel-thirsty machines falling, but the demand for economical sedans has pushed up prices for smaller cars.

Here are the numbers:

J.D. Power and Associates reports that prices for used Ford F-150 pickups have fallen 5.6 percent from a year ago.

At the same time, prices for used compacts such as the Toyota Yaris have risen more than 7 percent from a year ago.

What do you do about getting rid of that big SUV?

Like the stagnant housing market, where there are still some sales, some used SUVs are selling. But they tend to be vehicles priced at such a bargain that it makes little difference if they get just 14 miles per gallon.

Sellers should first look to making a private-party sale. Check Edmunds.com or the Kelley Blue Book site for the vehicle's market value and then plan on undercutting that number.

That's easier to do if you own the vehicle free and clear, or if even at a reduced value you're not upside down on the loan.

If you owe more than the vehicle is worth, resist the temptation to roll over the negative equity into that new economy car.

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Now more than ever, buyers need to have the best information available on the value of their trade. They also need to know the likely best deal on the new vehicle and to have the lowest possible finance rate in place before venturing onto a dealer's lot.

Even if you do finally unload that gas-guzzler, you'll still face a second challenge: finding a good deal on a fuel-sipper.

With gas prices still on the upswing, market conditions for customers wanting to move into something more fuel efficient are only going to get tougher.

The demand for new economical cars has gotten so hot that in a recent edition of the industry publication Automotive News, a dealer was advertising that it would pay the sticker price for Toyota Prius, Camry and Highlander hybrids.

If a dealer is willing to pay the sticker price to get a vehicle on its lot, you know that a regular customer is not going to be able to bargain much on the price.

Add in that some new car dealers are refusing to take full-sized SUVs and pickups in trades, and there's little doubt that a buyer looking to go from a gas guzzler to a gas sipper will have to pay a hefty premium.

So what's a shopper to do?

One suggestion is to shop brands other than Toyota, Honda and Nissan, the manufacturers who are usually the first stop for buyers looking for economy.

Korean manufacturers Hyundai and Kia are still hungry for sales, for example.

A 2009 Hyundai Sonata is being offered with a rebate ranging from $1,000 to $1,500. A 2008 Kia Optima carries a $3,000 rebate.

Suzuki, which is enjoying some of its best ever U.S. sales numbers, nonetheless is moving cars off dealer lots by offering rebates of $750 to $1,500 on the 2008 SX4 and $500 on its bargain-basement Reno sedan.

Here are this week's reader questions:

• Tips for unloading a gas-guzzling SUV • What should I do with 'tricked out' Acura? • Why won't the finance company pick up my car? • Do I need to use premium gas?

If you have a question for Terry, e-mail him at Driving for Dollars. Save money on your car -- sign up for Bankrate's new weekend Car & Money newsletter.