ROME, Italy—It was never going to be a bad car, was it?

You would no more expect McLaren’s new 720S to be a dud that you’d expect Stephen Hawking to come out with a theory that the universe was created yesterday, or that Frank Gehry’s next building would be a simple rectangle.

That knowledge still doesn’t prepare you for just how good the 720S is. Although, it’s not exactly what you imagine either.

The 720S is a replacement to the 650S – still not very creative with the names, eh, McLaren? – the first in a new line of Super Series cars. It sits in the mid-range of McLaren’s lineup, above the Porsche- and Audi-baiting 570S and GT, but below the multi-million dollar P1, which is sold out.

Over the coming years the 720S will spawn a drop-top variant, perhaps a touring-focused GT model, and – last but not least – a race-y LT towards the end of its life-cycle.

Revealed publicly at the Geneva Motor Show in March of this year, the 720S is important because it’s McLaren’s first second-generation car. It shows how the young brand will mature its products.

Visually, the 720 is striking, even by supercar standards. McLaren takes a form-follows-function approach to design. The two gaping nostrils on the front of the car, surrounding the headlights, are a love-it-or-hate-it detail.

Admittedly they look much better in the flesh than they did in those first few photos. Like every shape on the 720S, the nostrils have a purpose: they suck in fresh air for the low-temp radiators mounted at the front of the car.

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Moving to the side, you’ll notice there are no huge vents on the car’s haunches as you’d typically find on a mid-engine car. McLaren has hidden the air intakes inside the double-skinned doors.

Other aerodynamic magic? That new full-width active rear wing acts as an air brake under heavy braking, and can pop up in less than half a second. McLaren’ claims the 720S is twice as aerodynamically efficient (downforce-to-drag ratio) as its predecessor.

There’s a lot of P1 in the new design. It’s organic-looking, shrink-wrapped around the mechanicals but with a cohesive flow that the P1 was lacking. I think the 720S is McLaren’s best design to date.

It’s like sitting inside a very small greenhouse. There’s glass everywhere. The 720S is based around a new carbon-fibre monocoque – not just a tub this time – which includes the roof and pillars.

Carbon fibre is so strong and light the pillars can be unusually thin. Looking over your shoulder, the C-pillars are split by a glass panel, letting you see through it. Look up and even the tops of the doors are glass. Outward visibility is excellent.

From a hidden latch, the dihedral doors swing upward and forward. The opening is huge, because the doors incorporate a big chunk of the roof on either side of the car. It looks cool, yes, but there is a practical benefit: there’s no danger of smashing your head against the roof while getting in or out.

Once inside, the cabin feels compact and narrow, although the actual ergonomics are perfect. There’s a luxuriously finished leather cargo shelf behind the two seats, above the engine.

McLaren says there’s enough space back there to fit an airline carry-on bag. Be sure to strap it down tightly; you don’t want to watch your luggage go flying through the front window when you stomp on the brakes.

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Chris Goodwin, McLaren’s chief test driver, said working on the 720S’s new suspension setup was “easily the most complex thing I’ve done at McLaren. And, ironically, it’s something you won’t feel. It’s not something that’s switching on and off.”

He’s talking about the hydraulically-interlinked dampers, an evolution of the system on the 650 and P1 that lets McLaren do without anti-roll bars. The new system has sensors directly on the dampers and unsprung mass. They feed better data to the car’s brain, where a new algorithm developed over several years with Cambridge University calculates how best to “grind the tires into the road.”

Combined with a revised rear suspension setup – stiffer, with less bump steer and increased toe-control – it makes the car feel stupendously stable where a mid-engine car should be anything but.

Other tech highlights include a Variable Drift Control system, and a new infotainment setup. The old IRIS system is gone. The replacement is visually slick, quicker to respond, and only lagged on occasion. A big improvement then, but still not quite perfect. The flip-down dashboard screen is a neat party-trick too.

Some of the routes around Rome are among the oldest in the world. And they feel like it: rotten, rutted, rippled pavement everywhere you go. An odd place to launch a supercar.

Thankfully, the all-glass cabin means it’s easier to spot rogue scooters buzzing all around than it would be in, say, a Lamborghini Huracan, or even Ferrari’s 488.

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The 720S handled the roads with uncanny grace. In such a low-slung supercar you instinctively brace-for-impact before an unavoidable rut, but when the 720 rides over it, you think, ‘that wasn’t so bad.’ And it happens again and again.

The 720S is more compliant than anything in its class. The clever hydraulically-linked dampers separate impact stiffness from roll and dive stiffness, so you can have a car that’s softer over crappy Roman roads and yet still razor-sharp on a race track, which is where we were headed.

The Autodromo Vallelunga Piero Taruffi, about 30 kilometres north of Rome, is a mighty fast, flowing track with a huge range of camber and corners.

After the home straight is a left-right-left S bend that you turn into at about 200 km/h. The car gives you the confidence, feeling so stable with all the aerodynamic and mechanical grip.

From what I remember of the 650S, it felt loose under braking, by comparison. Goodwin is right. You don’t notice the clever suspension system per se, only that the 720S is pinned-down in high-speed maneuvers and extreme braking.

The acceleration, of course, is glorious. The new 4.0-litre V8, twin-turbocharged, makes 710 horsepower and 568 lb-ft of torque. From a standstill to 100 km/h takes 2.9 seconds, while zero to 200 takes just 7.8. That’s 0.1 seconds faster the McLaren’s track-focused 675LT.

The engine is happy to rev out to over 8,000 rpm. You don’t feel like you should be short-shifting. The sound is a mix of turbine and machine-gun, but not quite spine-tingling, even with optional sport exhaust.

Variable Drift Control is an adjustable traction control system which allows you to vary the degree of slip before it cuts in. Getting the 720S to slide takes a big dollop of power to overcome slight steady-state understeer. It’s not set up to be loose and playful like the 570, though it will drift if you have ample skill and commitment. The 720 feels more comfortable going fast, with a few degrees of oversteer powering out of corners.

The chassis feels so responsive through the wonderful hydraulically-assisted steering, but also through the carbon brakes and throttle. With every input you can feel the car react, predictably, instantly.

“The idea of our cars is to make them feel natural,” says Goodwin. The 720S pushes the envelope far and fast.

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The 720S starts at $312,500 in Canada. Two different cosmetic packages – Luxury or Performance – can quickly bring the MSRP up to $324,980. You can easily spend tens-of-thousands on carbon-fibre bits, and the sky’s the limit once you dip into custom McLaren Special Operations options.

The key rivals are the Lamborghini Huracan and the Ferrari 488, the current class benchmark. The Ferrari costs a few grand less, but in this price bracket that’s pocket change.

The 720S is a precision instrument, a true driver’s car. It’s honest and pure at the limit and below, the kind of car that will teach you to be a better driver.

There’s a depth to the 720S ability that makes it more than just a play-thing. And yet, it’s remarkably comfortable on city roads. This broad appeal, for me, makes it the new car to beat in this class.

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Disclosure—This writer’s travel and accommodations were provided by the automaker for the purposes of this first-drive review.