The Range Rover Evoque convertible is a hybrid, but not in the traditional sense. Part truck, part sports car, straddling the line between hillbilly and city slicker, it’s half fish and half fowl.

The resulting vehicle is a two-door, four-passenger sport utility vehicle that the Range Rover company calls a “crossover with capability.”

Driven by a 2.0-liter turbocharged four-cylinder engine that makes 240 horsepower and 250 pound-feet of torque, the all-wheel-drive Evoque convertible comes equipped with a suite of electronics to ensure that capability.

The Terrain Response System enables the Evoque to master mud, sand, snow and other surfaces. The Hill Descent Control keeps the Evoque from running downhill, while the Hill Start Assist keeps it from slipping from a dead stop while pointing uphill.

More electronic aids – including traction control, roll stability control and dynamic stability control – keep the Evoque secure on flatter ground.

This feathered fish is a bit anonymous around town when the top is up. But it’s entirely anomalous when the top is down.

“That car is sick!” one fellow commuter called out to me. “It’s a total babe magnet!” said another.

Not everyone appreciates the anomaly. One friend grimaced when I pulled to the curb, noting the car’s high belt line and short wheelbase, and said, “It looks like a hot tub with a windshield.”

Like everything in the Range Rover family, the Evoque (base price $58,270) is a pleasure to drive. Competent and easy to park in town, it feels lush on the freeway, solid and planted.

The engine chugs through a nine-speed automatic transmission, which may help with fuel economy but felt like three or four too many gears for smooth driving. (That transmission is also in the Jeep Cherokee cars, which produce a similar sensation.)

I experienced a little turbo lag when I went pedal to metal, before that torque kicked in and pushed the Evoque forward.

The suspension works to do all things well, but doesn’t. A little stiff around town in Normal mode, it begins to feel sporty in Sport but remains a little too soft to inspire confidence off-road, where the relatively limited ground clearance and thin tires prohibit it from getting too rowdy in the rough stuff.

Built on the same platform as Range Rover’s Discovery Sport SUV, the Evoque shares its engine and many other characteristics with that Sport and also with the sibling Jaguar XE sport sedan.

The Oxford leather front seats are cozy and comfortable. On the model I borrowed, they were heated too, but not ventilated. The similarly upholstered rear seats, while not spacious, are also comfortable and allow ample head room with the top up or down.

Unlike many convertibles, the trunk offers enough cargo space – 8.8 cubic feet – to carry a golf bag around town, with the top up or down.

And that top? It features the second quietest, smoothest convertible motor I’ve ever encountered, after the Rolls Royce Dawn. It is so silent I had to keep looking to make sure it was actually doing its job.

It’s not clear who this car is for. The Jaguar Land Rover folks told me Evoque buyers are cross-shopping Jeep Wranglers, Audi A5 Cabrios and BMW 4 series convertibles.

Are there many of them? Yes, and no.

An executive with the company said the Evoque got to 100,000 units globally faster than any car in Range Rover’s history. Like the Discovery family of cars, it has been especially popular in the U.S.

But of the three models offered – the convertible, and two-door and four-door hardtop versions – the convertible accounts for only 7 percent of total sales, Range Rover said. Even though the Evoque convertible is the only soft-top Range Rover or Land Rover available, almost everyone is buying the four-door.

That makes more sense, but it’s likely to be less fun, and turn fewer heads.