Rolls-Royce’s new Dawn convertible is a sign that there’s still a market for top-down driving among people with 300,000 euros ($335,000) to spend on a car.

The BMW AG brand unveiled the two-door model in a webcast on Tuesday after a decade of declining industrywide sales for open-top cars. Mass-market consumers who want something sporty may have switched to SUVs, but the ultra-wealthy can have both. Three convertibles targeted at this kind of buyer will make their debut next week at the Frankfurt International Auto Show: the Dawn, the Ferrari 488 Spider and a rag-top version of the Mercedes-Benz S-Class.

Once synonymous with freedom and rebellion and available in every price class, open-top cars are becoming playthings almost exclusively for the rich. And there’s enough money at the disposal of the world’s elite to prompt Rolls-Royce to develop the Dawn.

“The ultra-wealthy will buy this car,” said Tim Urquhart, a London-based analyst at market researcher IHS Automotive.

Sales of convertibles have plunged 51 percent from their 2004 peak, to 409,770 cars last year, while sport utility vehicle deliveries increased nearly fourfold to 12.3 million, according to data from IHS. Though new convertible versions of the Ford Mustang, Chevrolet Camaro and BMW 2-Series may help nudge those numbers up by 2020, sales won’t return to the 2004 level, Urquhart said.

“We see very good potential” for four-seat convertibles, Rolls-Royce chief Torsten Mueller-Oetvoes said in the webcast. “We’re convinced you need to offer more space in the back of the car.”

Affordable convertibles have become increasingly hard to find. Volkswagen AG is killing off the mass-market Eos. Renault SA halted production of the Wind and the ragtop version of the Megane. Ford Motor Co. put the Thunderbird on ice in 2005 and today only sells convertibles as part of its Mustang range.

China Focus

Part of the decline in convertibles stems from automakers’ shifting focus to China, where high-end buyers wouldn’t dream of driving through smog-polluted cities in an open car. With the Chinese car market declining, however, this might not be such a bad time to unveil a niche model that’s not targeted at the country, Urquhart said.

“The Chinese market is currently seeing quite a contraction in the luxury goods business, and that isn’t only true for cars,” Mueller-Oetvoes said in an interview with Bloomberg Television today. “Of course we’re also affected by that, I must even say quite substantially. It’s hard to say how much we can compensate that in the rest of the world.”