Nor should P85D users be any more susceptible to range anxiety than owners of more conventional Model S editions. Tesla claims that the car's digital power controls can utilise two motors more effectively than one - so there's actually a modest gain in range over the old rear-drive P85. It's now 300 miles, just 10 miles shy of the regular 85.
Incidentally, the new model sits on top of a revised range, where the twin-motor four-wheel drive set-up (identified by the 'D' suffix) is also available as a £4100 upgrade to the regular 85. That edition gets a regular 50/50 power split between front and rear axles, though, with the same combined output as the 85. In the meantime, Tesla has quietly dropped the rear-drive P85 from the line-up; its reasoning is that anyone who wants the extra grunt will be happy to pay for the four-wheel-drive model that can make better use of it.
What's it like?
To activate the P85D's full potential, you press a button on the huge central touchscreen marked (and I'm serious about this) 'Insane'. And that's pretty much how it feels. Tesla's acceleration test track was a well-abused mixture of greasy cold asphalt and coarse gravel, but the P85D still managed to deliver a level of acceleration that would be difficult for anything else to match in the same conditions. It's the initial punch that does it - the kind of uncompromising shove from 0-30mph that comes with the torque characteristics of electric motors in general, now mixed with four-wheel drive.
What's missing, of course, is any sort of soundtrack. There's none of the sense of occasion that you get with a 458 attempting similar feats - or anything approaching the aural pleasure that can be delivered by a hard-worked AMG V8. Instead, you hear a distant whoosh as the twin motors kick in, accompanied by - and this is perhaps oddest of all - the sounds of the tyres themselves grabbing hold of the surface beneath them (on a dry road, presumably, you'll not even hear that).
Once you're up and running, there's even less standing in the way of the P85D's colossal torque; you'll need to be well beyond the UK speed limit before you'd detect any discernible reduction in the car's ability to gain momentum.
Try to carry too much speed into a corner and the P85D will simply understeer; behave yourself and the nose tucks in with more conviction than it does on the 85 (itself not a bad steer, by any measure). Regardless of how hard you're pushing, it stays admirably flat in corners - and there was enough compliance to dial out the worst road surface imperfections on Tesla's Norwegian test route.
There's still not much communication, though; you get three weights of steering to play with, but despite this, and regardless of the P85D's ability to thrill and delight every time the traffic lights go green, this is not a car that makes you feel truly connected to what the tyres are doing. In that respect, at least, the P85D feels like one of the family - a slightly more planted and considerably quicker stablemate to the 85 and 60.
The same can be said for refinement, really, because the large alloy wheels still create a fair amount of road roar once you're above 40mph. It's by no means noisy aboard the P85D, but nor is it as silent as you may expect a fully electric vehicle to be.
The cabin remains a clever bit of packaging, with room for five adults and potentially two further children in rear-facing seats in the boot. The luggage capacity is still enormous, with space under the bonnet and in the traditional boot totalling almost 1800 litres. The finish on materials is of a remarkably high standard compared with any other American car - although a few elements are half a notch behind the best European executive models when you get to a close-up inspection.
The showpiece of the cabin is still the Model S's gargantuan centre screen, a 17in behemoth of a touchscreen through which you control the majority of the vehicle functions, let alone infotainment or navigation. It's still a bit worrying to see the system redrawing chunks of map as it struggles to keep up with sheer amount of real estate it has at its disposal, and there are occasions when you'll wish they'd just fitted a permanent button - Volvo's new system on the XC90 does a better job of fast-tracking you to regularly used functions - but in the most part it's a triumph.
Tesla has also rolled out the music streaming service Rdio to its cars via an over-the-air upgrade. In theory, the system allows you to press a steering wheel-mounted button and request any song - and voice recognition and a data connection will do the rest. In practice, you may find the search facility and data speeds more limiting than your own imagination.
Should I buy one?
If you're in the market for a Model S - and we can think of plenty of reasons why you could be - then it's going to be hard to resist the all-round performance increase and all-weather ability of the P85D. It does feel noticeably quicker and a little more secure than a conventional 85, and the four-wheel drive means that it stands a chance of keeping you moving on those three days a year where the weather grinds Britain to a halt.
You're paying a fair old premium, though; the four-wheel-drive 85D is still a car that can crack 0-60mph in just over five seconds, and there's a £14,000 hike from that car to the Ferrari-rivalling pace of the P85D. Even if you finance (the most appealing way into a Model S, realistically), you're looking at a premium of around £300 per month for a couple of seconds off the 0-60mph time.
Many will look at the raw figures, do the maths and, with a tinge of regret, allow head to overrule heart. Those who don't will be picking one of the most remarkable production cars on sale today.
Tesla Model S P85D
Price £79,080 (after £5000 government grant) Engine Two electric motors Power 682bhp; Torque 687lb ft; Gearbox Single-speed, direct drive; Kerb weight 2238kg; Top speed 155mph; 0-60mph 3.2sec; Range 300 miles; CO2/tax band 0g/km/0%