The Audi RSQ3 is a 400bhp grille with a mini-SUV attached

Attention, anyone with OCD triggered by the old Audi RSQ3 only having one massive oval tailpipe instead of the signature two RS pipes. We have good news. Meanwhile, anyone who’s sick to the back teeth of coupe-SUV-crossover-4x4 niche-o-thingys: go and pop the kettle on.

This is the new Audi RSQ3, and its 45mm lower twin, the RSQ3 Sportback. That’s the green one, with the letterbox slot for a rear window. And look! Both bodystyles have the full complement of two giant tailpipes. Symmetry rules.

At the front, you get almost no bodywork. Instead, you get a sort of chain-link fence, so it looks like you’re driving around in an Area 51 security booth. A really fast one.

Somehow, despite pressure to cut carbon emissions and Hybridise All The Things, Audi has kept the five-cylinder engine alive for its super-Qashqai. Yep, the RSQ3 and RSQ3 Sportback boast a 2.5-litre, five-cylinder engine that’s turbocharged to deliver 394bhp and 354lb ft.

A seven-speed twin-clutch gearbox and some quattro all-wheel drive later, that power arrives at the road and launches the RSQ3 from 0-62mph in 4.5 seconds. Hmm, sounds conservative. Bet it’ll go quicker.

Some time later, the ultra-Q3 tops out at 155mph. Pay Audi and it’ll kindly raise the limiter to allow 174mph. Does the world need a school run hatchback-on-tippytoes that can out-drag a Ford Mustang or Porsche Cayman? Answers on a digital postcard.

Will it be a lumbering nose-heavy anchor? No, says Audi: this version of the five-pot motor is 26kg lighter than the last one, and it’s already proved to be noticeably less leaden in the Audi RS3 and Audi TT RS.

Will it shake your teeth loose from your gums? Well maybe: you can spec 21-inch wheels for max pose/minimum ride comfort, but instead of the 10mm lower sport suspension you can spec adaptive ride with a Comfort Mode. Phew. There are also ceramic brakes on the options list, but only for the front wheels. Because ceramic discs out back on a family crossover is just stupid. Even for Audi.

Inside, it’s a world of high-contrast stitching, ambient lighting and high-res screens, but the RSQ3 Sportback doesn’t declare war on headroom as badly as you might think. Audi quotes 530 litres of boot capacity for both cars too.

Because hey, you’re buying a taller version of a hatchback with a sloping roof so it looks sporty and packs as much power as a Ferrari 360, but you don’t want it to be impractical. Have we got this right?