A couple on a scooter peer into our car as we wait by the traffic lights. They compliment the bright blue Mini Convertible as the girl jovially asks if she can finish our ice cream. It is a strange request, granted.

Yet cruising the expansive ocean road on the outskirts of Lisbon, roof lowered soaking up the Portuguese winter sun, the spirited Torre de Belém and Atlantic in full view, it feels almost natural to hand over a half-eaten gelato. This is what cars like the Mini do. Their unashamed retro-ness prompts a sense of nostalgia – perhaps in this case for more innocent times when ice cream sharing was de rigueur.

This is Mini’s third-generation Convertible since the marque’s rebirth under the BMW Group. Like the latest version of the hatch, which was launched last year, the fabric-roofed sibling is a consciously more adult car. For a start, it forgoes some of the more playful interior elements – the bubbly door knobs, oversized dials and so on – for more sober features.

In truth, it was time for the Mini to grow up. The retro cuteness felt a little self-conscious – forced, you could say – and was in danger of becoming an empty pastiche of the original Issigonis car. The Mini had become a victim of its own global success – and perhaps the Munich management felt too comfortable to make too many fundamental changes.

The slightly conservative approach works. The Mini is a more expensive car than those that share its size, and for this alone it must offer a more exclusive package. So everything we see, feel and smell are noticeably more premium; a bigger package of kit is now offered as standard, and there is a much bigger emphasis on personalisation too.

Measurements have increased all-round compared to the previous model – it's now 98mm longer, 44mm wider and 1mm higher. A 28mm longer wheelbase offers noticeable extra legroom for all passengers, and there is 36mm more legroom in the back, even if the second row remains a mighty tight fit. Then again, the Mini Convertible isn’t setting itself out as a practical family car – it is a car for two, with perhaps a small child, and with enough room to offer a lift to a friend.

Like the previous model, the boot-lid is hinged at the bottom for a split-tailgate and an opening top deck for easy access – the former looks great and is also practical, supporting up to 80kg. The cargo area now offers some 25 per cent more space at 215-litres, reduced to 160-litres with the roof lowered.

The dash remains distinctively Mini but is more refined, with a 6.5-inch display infotainment display screen offered as standard with Bluetooth and Mini Connected services, parking sensors and a reversing camera.

The main design advancement is with the fabric roof construction; one of the outgoing model’s shortcomings was the lack of visibility with the roof lowered as the bulky fabric sat a little clumsily above the rear seats.

This is no longer the case. The fully electric folding roof goes up and down in a reasonable 18 seconds and at speeds of up to 18mph, and there is the handy sliding sunroof option that can be activated at any speed. With new roof acoustic insulation it is also noticeably quieter inside the cabin with the roof up – as we got to experience on the second day, the sun sliding behind clouds for a furious Atlantic rainstorm.

The handling is noticeably smoother and faster especially, in the Cooper S we drove; the engineers have optimised the stiffness so it has grip and go, retaining the go-kart feeling that is so integral to Mini's identity.

An entry-level Mini One variant is expected to launch later in the year, as is a range-topping sporty John Cooper Works. For now though, the marque is offering the Convertible range in three options – the turbo petrol Cooper, turbo diesel Cooper D and the Cooper S with 189bhp from a 2.0-litre turbocharged petrol engine.

Customisation options now include two new exterior colours – a Melting Silver and the bright Caribbean Aqua that we drove, and the Union Jack pattern can be delicately woven into the back of the headrests, if this is what the customer so wishes.

A special Open 150 Edition – of which 150 models will be available – is also available to order this month. It features a special leather upholstery and paint combination, exclusive dash plaque, Chili Pack and Media Pack, including LED headlights and satellite navigation.

Mini had started to seem constrained by its own creation; the compelling storyboard sketched for the marque in 2000 was beginning to restrict the design process, allowing for only minor evolutions. The new Mini Convertible may have taken a more traditional narrative route, yet it still manages to instill subtle humour, witty aesthetics, that element of surprise. Gone are the redundant metaphors though (perhaps bar the Union Jack); instead, we are offered a more considered car and a more intelligent machine that is still hugely fun to drive.

A sobered up Mini is a nod to maturing motoring habits – yet still young enough to invite ice cream sharing with strangers on a Portuguese street.