The answer is pretty much the same as what they have been doing - making the quirky and unpredictable British films that strike a chord beyond the UK, and in particular with American audiences: movies like The Crying Game, Trainspotting and Four Weddings and a Funeral.
In October, Miramax announced it was hiring 51-year-old Leventhal and two other top UK film executives to form an independent, London-based film production unit. All three have been central to the much-acclaimed renaissance of the British film industry.
Officially opening its doors on 2 February, the unit has provisionally been named HAL, an acronym inspired by the names of the three - Leventhal, his wife Trea Hoving and David Aukin.
For Miramax, the New York-based specialty film company owned by Disney Corp, such a move is unprecedented - the first time its hard-driving co- chairman Harvey Weinstein has loosened the reins and granted others authority over which films to make and how to make them.
The three HAL executives control a $50m (pounds 30.5m) revolving fund with the freedom to approve projects and make final editing cuts, plus another $3m for longer-term development. They also have assurances that whatever films they produce will be distributed by Miramax.
Such an arrangement is a rarity even in the US. "It seems to be difficult philosophically for American companies to grant any real autonomy in their offshore divisions," said Simon Perry, chief executive of British Screen Finance, the film funding organisation partly supported by the Government. "At the end of the day, they become fax operators," he said. "They have to get approval from LA."
So what has changed? "Frankly, the UK is a happening place," said Leventhal, in an interview at Miramax's offices, a meandering former mews in Soho. The buzz about Britain means that UK products are perceived as more desirable around the world, he said.
Other US studios have taken note. Fox Searchlight - which produced The Full Monty after Channel 4 rejected it - is considering a joint venture with satellite broadcaster BSkyB, an arm of Fox's parent, News Corp. Paramount has reportedly been trying to establish a British film division. MGM has recently based its independent production and acquisitions unit, Goldwyn Films, in London. Sony has a venture with The Bridge, a joint project with France's Canal Plus, to develop feature films.
Increasingly, US studios, with their heavyweight distribution and marketing capabilities, sense an untapped opportunity in Britain's film community.
Based on the eagerness with which he snapped up Leventhal and his partners, Miramax co-executive Harvey Weinstein obviously thinks there is potential. In September, Aukin and Leventhal were already several weeks into talks with Universal Studios about setting up a UK unit when Weinstein got word of the talks and wooed them away. Aside from creative licence, he offered them undisclosed equity interests in the unit.
Miramax has had a long, productive link with the British film community. The company has maintained a London office since the 1980s, with money and artistic control flowing from New York.
"Miramax has a terrific record of being here, scouting out talent, knowing everybody, reading everything, and slipping into screenings even if they're not invited," said John Newbigin, adviser to the Department of Culture.
The HAL unit does not reflect a significant increase in the amount of money Miramax is spending in the UK. In recent years, the company has spent about $40m a year in buying and producing British films, including The English Patient. It is currently making Tom Stoppard's Shakespeare in Love in London, with production costs of about $30m.
One open question is why the HAL team would agree to a project with only $50m of funding. In the world of commercial feature films, it's not much. Working Title Films, the London-based arm of Dutch entertainment company PolyGram - which last year made Bean - has an annual production budget of $150m and a development fund of $10m.
It's significant that the $50m controlled by HAL is not an annual figure, but the amount of a so-called revolving fund. This means that if HAL's films make money, the fund grows. If they don't, it disappears. Leventhal side-steps such questions, saying only that the $50m is what he and his partners requested. He said they will be trying to "co-finance and co- produce with other parties in the UK," but declined to be more specific.
At Channel 4, Leventhal and Aukin developed the station into a showcase for high-quality, critically acclaimed feature films, including Four Weddings and a Funeral, The Madness of King George and Secrets and Lies.
Hoving is a former acquisitions executive at Miramax. She's the one who decided to invest in The Crying Game, together with Channel 4. She also bought such art house hits as Like Water for Chocolate.
The British film industry is still hobbled by its size. The Full Monty, Four Weddings... and Trainspotting, which are the all-time top grossing British films, each cost about $3m to $4m to make. In the US $45m per film is the norm and Titanic cost well over $200m.
Smaller films do occasionally turn into blockbusters but most earn little if any profits. The way to be competitive in the long term, according to Thomas, is to make movies with bigger budgets and higher production values that are more likely to earn their money back.
Leventhal says he and his partners will continue to develop films in the $5m range but will also spend double or triple that amount on others.
One way the HAL team may hope to boost profits is by developing the merchandising side of the business. Leventhal says he plans to work with Weinstein to develop books, soundtracks and other products tied to the movies they make.
Does that mean we'll be seeing Full Monty mugs and Four Weddings... photo albums? Leventhal would not elaborate. "It's about making money," he said.
Copyright: IOS & Bloomberg