Infiniti, Nissan’s luxury brand, has had a thing for the letter Q that began with its first offering, the 2006 Q45, a full-size sedan with four doors. Today, Infiniti’s only cars are sporty two-door coupes dubbed Q50 and Q60. The SUV has taken over, and for them Infiniti borrowed the letter X from winter sports (X-country skiing, as opposed to downhill) and attached it to the letter Q.

Infiniti now sells four QX models, from the compact QX50 to the gargantuan 8-seat QX80. This one, the QX55, is the most intriguing of them. But if you need a vehicle for a family of tall teenagers, stop right here. The QX55 is for those whose kids have grown up and moved out—or young couples of sufficient means whose family planning goes no further than a dog. Not a Great Dane, either.

Although it has four doors, the company calls this new-for-MY2022 model a crossover coupe. That is, Infiniti applied the fastback silhouette of a sleek two-door car to a crossover sport-ute. Beneath the QX55’s elegant sheet metal lies the chassis and powertrain of the more pedestrian-looking QX50: a 2.0-liter turbocharged Four, a CVT transmission and front-biased all-wheel drive.

The engine is unique in that it automatically varies the length of the pistons’ stroke to adjust compression ratios from 14:1 to 18:1, for extra power (268 horsepower and 280 found-feet of torque) when needed or up to nearly 30 MPG in steady-state highway cruising.

Continuously variable automatic transmissions are rare in luxury cars—they tend to be noisy and unsatisfying to drive—but they’re stepless, so they contribute to economy by always being in the most fuel-efficient “gear.” Infiniti has ironed out all the CVT wrinkles here, and the 55 behaves like a proper car. Drivers who want something to do can play with the manual shift paddles on the steering wheel and also select Standard, Eco, Sport and Personal drive modes. Personal lets the driver program her own combination of shift points, steering effort and engine response and sound.

The QX55 has no on-road faults other than anesthetized electronic steering, but it truly shines in the style department. Photos don’t do justice to its svelte profile or the subtlety of its myriad folds, bumps and creases. The sophistication continues inside, with a rich-looking and well-equipped cabin that Infiniti boasts is “ergonomically supportive”: The screens are crisp and clear (reading glasses not needed) and the menu icons seem almost three-dimensional. The many possible adjustments are logical and easy to carry out. The informative HUD, head-up display, in the windshield can be moved higher or lower, brightened or dimmed, and even adjusted for tilt.

On top of its standard comprehensive driver-assistance features, our QX55 also gets ProPILOT, Infiniti’s optional semi-autonomous driving mode. It’s part of the range-topping Sensory trim package.

The base QX55, the Luxe, starts at $46,500. Next comes the Essential, which starts at $51,600, and then the Sensory, with an initial sticker price of $57,050. Ours, with “welcome lighting,” premium paint and a couple of other minor items, plus $1,025 in destination charges, topped out at $60,595. Such prices seem nearly normal these days.