When people think of Kei-cars, they tend to think of boxy wagons and quirky hatchbacks designed only for the Japanese market. With tiny 660 cc engines that qualify them for cheap tax and insurance, the Kei-car platform doesn't seem like a natural place to start when designing a sports car.

That didn't deter Honda from creating a mid-engine, rear-drive sports car to fit the strict yellow-plate rules.

The S660 was originally teased as a concept at the 2013 Tokyo Motor Show, but made it to production virtually unchanged. In the metal, there's a strong resemblance to the Honda Beat, one of Honda's pint-sized sports car from the past. Those low, wide headlamps mirror the Beat's lights, while the line that runs along the side is also a clear reference. The rear deck is short, with pronounced hips and small cooling louvres over the tiny 3-cylinder powerplant, while there are small cooling vents cut into the front flanks.

The S660 has even got Lamborghini Aventador style air intakes sitting over the driver and passenger's shoulders, and a tiny window between the rear buttresses that opens up to give you a better connection to the engine's turbo noises.

Sounds a bit gimmicky, but the little window is actually one of the best features on the car – we found ourselves giggling away as the little engine huffed and puffed its way through town.

Roof off, tiny rear window down and it was time to hit the open road ... and first impressions were good. The car's clutch is light and the gear ratios are perfectly spaced for making the most of the little engine's 63 hp (47 kW) as we zip between immaculately maintained taxis and boxy Daihatsus towards the Tomei expressway.

The S660's three-cylinder turbo engine is from Honda's N-Box, but it's been tweaked with new turbo geometry for better performance off the line and in the midrange. It sounds raucous and rattly as we buzz along, but it's got plenty of punch provided you keep it between 3,000 and 6,000 rpm.

While the S660 is performing perfectly, I'm not doing so well. With no data connection, Google Maps is having a minor freakout and at the Tomei Expressway's first toll booth, I pull up to a gate specifically for people with a prepaid toll card. I, being from Melbourne and not Tokyo, don't have that card. Cue an awkward exchange with a polite, gloved gentleman who runs across from the neighboring booth to take my money.

Eventually we get back up to speed, accompanied by some brilliant turbo noises between gear changes. With the engine right over your shoulder, you can hear everything that's going on back there, feel the warmth it's creating as you look over back to change lanes.

At highway speeds things are a little blustery in the S660's cabin. The top of my head pokes out above the top of the windscreen, which makes for plenty of buffeting at 100 km/h (62 mph).

It's worth keeping in mind the S660 isn't exactly designed to do highway miles with lanky foreign journalists behind the wheel. That said, it feels absolutely rock solid at high speed and the ride is compliant and comfy. There's also no feeling that you might be blown off the road by the big semi trailers blasting past, which is reassuring for the gangly gaijin behind the wheel.

Off the freeway, it's time to point the tiny Honda's nose at some bends – and what better place to do it than in the hills above Hakone. From the first corner it's clear that it takes a fair bit to ruin the S660's composure. The little Honda is perfectly neutral: once it's turned in, it just holds its line perfectly.

As well as being perfect for Tokyo's tight streets, that light steering means you can flick the car around on the tight roads around Hakone without too much awkward hand-shuffling on the wheel.

What's more, the S660's size makes it perfect for exploring narrow roads. Anything bigger would make you nervous about drifting across the lines on the seemingly never-ending blind bends around Hakone, but the little Honda's tiny footprint means you can move around in your lane and find a neat line without worrying about hitting something coming the other way.

The steering is light and direct, and the S660 stays flat when you throw it around. Because it's so light the suspension doesn't need to be rock solid to keep the mass under control, so the fact it's compliant and comfortable on the motorway doesn't hold it back when you're having a crack.

Highlight of the whole experience, though, is the gearbox. Honda has a reputation for making super-slick manuals and the S660's is no different. Shifting with the short-throw metallic gearstick is an absolute joy, and a reminder that paddles and power don't always equal more fun.

There has been talk about an S660 making its way to the US and other western markets with a bigger, 1.0-liter three-cylinder engine. While the car's size would be restrictive for bigger buyers, we're sure that Honda would find driving enthusiasts looking for an inexpensive weekend car that you can enjoy at legal speeds.

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