If you’re a macho bloke who likes his cars to be all raw and challenging, you’re not going to care much for the new Z4. You see, BMW has decided that it wants to attract a larger audience with the latest version of its two-seat roadster, which in these times seems a perfectly reasonable gambit. And it reckons the previous Z4 was just a bit too hardcore and petrolheady to appeal to the sort of person that likes more rounded roadsters such as the Audi TT and the Mercedes-Benz SLK.

So BMW has made the new car bigger and softer in terms of its driving experience in a bid to lure more women as well as men who care about looking good. The new Z4 is certainly easier to look at than the old one, with less dramatic sluicing along the sides and a nice plumping and widening of the back end. From behind, there’s a definite flavour of its bigger sibling the 6-series around the lights, and at the front the grille’s wide new kidneys are reminiscent of the company’s flagship 7-series. So the new Z4 is a grown-up-looking machine.

The biggest news about the new body is a folding metal hardtop roof, replacing the previous Z4’s fabric folder. It’s a two-piece aluminium structure that glides up or down in 20 seconds at the touch of a button. With the roof in place, the Z4’s profile is still elegant, although, as with the SLK, the roof structure looks a bit small in relation to the rest of the body.

The interior has been improved too. Thanks to the increased dimensions of the body, the cabin now has more shoulder and elbow room, and headroom has increased by nearly 2in. The glass area has increased as there are now two side windows instead of one, and that creates a much airier feel with the roof up, as well as better outward visibility. The dash centre also feels less imposing, and the rotary controls for heat and cooling are better presented than in the previous model. The quality of materials and their assembly looks first rate too.

When the new Z4 goes on sale in May, there will be a choice of three six-­cylinder engines, ranging from 201bhp to 306bhp. On the gearbox front you can have a six-speed manual, a conventional six-speed automatic or a seven-speed direct-shift transmission — basically, BMW’s version of Volkswagen’s DSG — on the highest-powered version.

We drove the top-of-the-range Z4 sDrive35i. This, BMW says, is the world’s first straight-six petrol engine to feature twin turbocharging. It develops 306bhp at 5800rpm, and 295 lb ft of torque, much of which is available at just 1300rpm. The maker says it’ll hit 62mph in 5.1sec. Which is pretty damn quick for a non-M-tuned BMW.

Once you’ve climbed into the Z4, you sit so low that your bum feels as though it’s barely clearing the rear axle (it is surprisingly close). The view over the swollen bonnet is classic long-nose roadster, although you’ll have no clue where the nose ends because it dives out of sight.

When you prod the ignition button the engine woofs into life and you lower the roof. Which you may do only when the car is stationary, because when the bootlid swings up to accept the roof, the third brake light can’t be seen, and that’s against European law. Not exactly brilliant, when the soft-top Audi A5 cabriolet, for instance, can drop the roof at up to 30mph. Also disappointing, the Z4 is remarkably noisy at speed with the roof up, a combination of tyre roar and wind rustle. That surprised me.

Then, a little play with the steering-wheel-mounted controls for the double-clutch gearbox. When you downshift, the throttle blips itself to match the revs of the lower gear, and when you upshift under full throttle, there’s the most delicious little rumble on the overrun as the next ratio comes up. These shifts happen instantly, with virtually no break in the power delivery. It’s faster than any human hand could match with a manual gearbox, and when you’re on wide-open throttle, the Z4 feels mightily swift. In a straight line.

There’s another thing BMW has done to tame the previous Z4’s hardcore profile. That car was quite a decent drive in its final iteration but it didn’t offer the most compliant ride. So on the top model of the new car, BMW offers something called Adaptive M Sport suspension. This affords three settings: normal, sport and sport+.

How well does the system work? As you go up through the modes, throttle response and gearshift speed increase, which makes things feel nicely urgent. Push hard in normal mode and the Z4 lacks body control; the back end feels loose — and not in a good way. Sport is better, but this is still not a car that you’ll push hard for the fun of it. With sport+, you get a more punishing ride but without much added fun. And you begin to feel the extra 100kg the new Z4 is carrying on a twisting road. Not exactly the “ultimate driving machine” promised by BMW’s advertising, then.

The bottom line is, if you really like driving, buy a Porsche Boxster. It’s a proper sports car and it’s cheaper than the £37,060 Z4 sDrive35i.