Auto makers are working harder these days to woo drivers who care about size as much as mileage.

Discounts on crossovers — which are built on a car’s frame but styled like a sport-utility vehicle — are at their highest level in two years.

Car shoppers can find a bevy of deals on crossovers, including cash-back offers ranging from $500 to upward of $4,000. Auto makers also are using low-interest-rate deals and subsidized leases to lure buyers. The average incentive on a crossover in July was $2,437, the largest since September 2006, according to Edmunds.com, an auto research firm.

Crossovers offer a reasonable alternative for SUV owners who still crave space and can’t fathom hauling around the family in a subcompact. In addition, improved mileage, while not exemplary, can land in the 25-miles-per-gallon range, 10 mpg ahead of some larger SUVs. Many of the vehicles offer four-wheel drive along with other bells and whistles, and they handle better than larger SUVs.

Last month, Katie Milette, a 52-year-old married mother of three in Laguna Beach, Calif., wanted a new hybrid, a model that is partially powered by an electric motor. As Mrs. Milette shopped for lower emissions and better mileage, another factor came into play: She and her husband needed room for camping and ski gear when they meet their grown children for family vacations. She settled on a Mercury Mariner hybrid crossover. “We’re kind of the stuff-carrier, we’re taking all the gear,’’ she said. “Because of that, we want one car in the family that can do that.’’

Still, when gasoline surpassed $4 a gallon, consumers rushed to small cars and stopped buying crossovers. Crossover sales fell 11 percent in July from a year ago, according to Autodata Corp., the fifth consecutive month of declines. Overall, crossover sales are off about 4 percent this year. Even though they get better mileage than SUVs, most don’t crack the 30 miles a gallon many consumers have craved in recent months.

“Anything perceived to be large and a consumer of fuel is going to be deemed a little suspect right now,’’ said Jack Nerad, editorial director of Kelley Blue Book, a firm that gives consumers pricing information and other data on new and used cars.

In that climate, small-car sales have skyrocketed, up about 11 percent through July. Luke Matthews, a 30-year-old information-technology worker in Madison Heights, Mich., just traded in his Dodge Caliber crossover for a new Ford Focus compact car, which can get about 35 mpg. He made the switch even though his Caliber got fairly good mileage.

“I wanted something that got at least 30 miles to a gallon,’’ he said. “I need something that’s not going to break my wallet every day.’’ He said he might consider a crossover again if gas prices come down, but would prefer that auto makers improve their fuel efficiency instead.

Despite the stampede to small cars, crossovers don’t appear headed for a permanent decline like SUVs. Dealers and industry analysts say the market shift to small cars has receded slightly in recent weeks as gas prices have moderated a bit.

Prices on crossovers range from less than $20,000 for smaller models like the Chevrolet HHR to more than $35,000 for larger luxury models like the Lexus RX 350. Many crossovers can be had for prices comparable with midsize sedans.

Even if demand picks up, crossover discounts are likely to remain. For one, manufacturers keep introducing new crossovers to feed what was until recently a white-hot segment. The competition from that oversupply, combined with still-high gas prices and year-end model clearances, means auto makers will be gunning to grab market share, says Mike Maroone, chief operating officer of AutoNation Inc., the nation’s largest dealership chain.

“I think they’re going to have to do whatever it takes to liquidate the ’08 inventory,’’ he said. “It’s going to be aggressive.’’

Indeed, General Motors Corp. just offered employee pricing, on top of existing rebates, for nearly all its 2008 models and some 2009 vehicles through today. The move could force other auto makers to respond in kind. For consumers looking at GM’s crossovers — the Buick Enclave, GMC Acadia and Saturn Outlook — the promotion means discounts totaling about $3,800, a spokesman says. Regular prices on those crossovers can push $30,000.

Shoppers in some areas can likely get Ford Motor Co.’s Lincoln MKX with all-wheel drive for about $33,000 after about $3,500 cash back, according to Edmunds. Alternatively, you can get zero percent financing for 36 months or a meager 1.9 percent for five years. (Nearly all prices and discounts vary by region. In some cases, additional cash-back offers not counted by Edmunds boost discounts even higher.)

A Ford Edge can be had for under $23,000 after some $3,750 in rebates, depending on the circumstances. Toyota Motor Corp.’s Highlander has $1,000 cash back on it in many areas, pushing the total payout down to around $28,000.

For leasers, there are sporadic attractive deals. Detroit auto makers are scaling back leasing amid plunging resale values for SUVs. That could open the door for foreign auto makers to sweeten their lease offers in the coming months.

Now, consumers can lease a Nissan Rogue for $229 a month for 24 months in many cases, according to Edmunds. A Toyota RAV4 with a four-cylinder engine and all-wheel drive can be had for $199 a month over 36 months.

Some crossovers lack discounts but still go for reasonable prices. Sales of the Honda CR-V were off about 13 percent in July, but it remains the top-selling crossover, and one of the top-selling vehicles in the U.S. overall. Customers can likely get one with all-wheel drive for under $22,000.