The 2013 Toyota RAV4 has a redesigned exterior, with its spare tire moved from the rear door to a new home under the cargo floor.

It’s all crossovers these days.

From the polo grounds of Malibu to the campgrounds of Maine, nearly a fifth of all vehicles sold in the U.S. last year resided somewhere in this netherworld between a car and an SUV.

So the stakes were high for Toyota’s overdue redesign of the RAV4, a pioneer of the segment in the mid-1990s that had grown stale in comparison with competitors. Often resembling small sport utility vehicles, crossovers are truck-like vehicles built on front-drive car platforms.

The 2013 RAV4 is rolling into dealerships now. Although it’s plenty functional and more sporty than past Toyotas, it can’t match the rapidly improving sophistication of such vehicles as the Honda CR-V and Ford Escape.

With the RAV4, as with other models, Toyota is looking to shed its reputation for boring vehicles by injecting more dynamic performance and styling. But the execution in the RAV4 is hit-and-miss.

More emphasis on both sport and utility at times comes at the expense of comfort and refinement. And the guts of the RAV4 — the engine and transmission — are only slightly improved. The four-cylinder engine remains unchanged, and a six-cylinder option is gone. A new six-speed automatic transmission is more fuel efficient but hardly sporty.

The RAV4’s handling feels more athletic, with communicative steering and surprisingly stiff suspension for a grocery getter. That’s an upgrade compared with the numb feel of many past Toyotas. But the RAV4 overdoes it, making the ride too harsh.

The vehicle’s styling, inside and out, also falls short of the mark that Toyota has set for itself. The exterior improves on the forgettable presence of the previous model, but the sharply angled taillights and odd nose and grille of the new RAV4 make it seem more down-market and utilitarian than Toyota intended. One wise change was swapping out the old side-hinged rear door setup for one that swings up.

The interior is functional enough. Firm seats with thick side bolsters hold you comfortably in place. There are myriad storage cubbies, pockets and compartments throughout the cabin. The rear seats fold flat and can easily swallow a mountain bike without removing its wheels. But buyers will find competing cabins more hospitable and polished.

Under the hood is the same 2.5-liter four-cylinder engine from the outgoing model, now making 176 horsepower and 172 pound-feet of torque. An all-wheel-drive RAV4 will do zero to 60 mph in 9.1 seconds, according to Edmunds.com.

Toyota has unfortunately ditched the previous RAV4’s available V-6 engine, which distinguished it from many competitors by offering an impressive 269 horsepower and meaningful towing capacity.

The big mechanical change is the RAV4’s new six-speed automatic transmission replacing the antiquated four-speed gearbox of yore. The extra speeds give a nice bump to the RAV4’s fuel economy ratings.

Front-wheel-drive models have estimates of 24 mpg in the city and 31 mpg on the highway, while all-wheel-drive RAV4’s are rated at 22 mpg in the city and 29 mpg highway, according to Environmental Protection Agency ratings. In 340 miles of mixed driving, we averaged 23 mpg in an AWD RAV4.

But the transmission seemed to constantly hunt for the best gear, and the shifts seemed delayed at times. This was mitigated somewhat by the RAV4’s Sport driving mode, which also sharpened throttle response, though likely at the expense of gas mileage.

A base RAV4 LE starts at $24,145, including the destination charge. This buys you power everything; a 6-inch color display for the stereo and backup camera; stability and traction control; and eight air bags. The XLE trim we tested is just $990 more and includes a moon roof, 17-inch alloy wheels and dual-zone climate control. Options including all-wheel-drive and a package that includes touch-screen navigation, Sirius satellite radio and Bluetooth pushed the as-tested price up to $27,565, still competitive in the segment.

At the top of the lineup is the Limited model, which comes with features such as heated leather seats and a power tailgate.

The automaker expects to sell at least 200,000 copies in 2013. Given that it sold 175,000 of the outdated model in 2012, Toyota probably will hit its goal with the new version.

Meanwhile, the crossover segment continues to grow, with almost every automaker offering one. In 2012, crossovers made up 18.5 percent of all vehicle sales in the U.S., up from 8 percent a decade earlier, according to Edmunds.com. In the same period, market share of traditional truck-based SUVs fell to 6 percent of sales from 13.5 percent.

The increased competition and sales has pushed the levels of refinement in crossovers well beyond where they were in the 1990s, when Toyota helped define the segment with the first RAV4. Current versions of the Ford Escape, Honda CR-V and Chevy Equinox have set a high bar for others to match.

The changes to the new model only make the RAV4 relevant, not dominant. It’s functional and more fun, but at the cost of comfort. So in an era when crossovers have become the first choice for many families, Toyota still has some catching up to do.

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2013 TOYOTA RAV4:

—Vehicle type: 4-door, 5-passenger compact crossover SUV

—Powertrain: 2.5-liter four cylinder engine, front-wheel-drive or all-wheel-drive

—Transmission: Six-speed automatic

—Horsepower: 176

—Torque: 172 pound-feet

—0 to 60 mph: 9.1 seconds for the AWD model, according to Edmunds.com

—EPA fuel economy: FWD: 24/31 mpg city/highway; AWD: 22/29 mpg city/highway

—Base price: $24,145

—Price as tested: $27,565

—Highs: Crisp handling, practical cabin

—Lows: Harsh ride; interior is outclassed by peers

—Los Angeles Times’ take: A sportier Toyota that puts function before form

All prices include destination charges.