Italian Culture Minister Francesco Rutelli has swaggered into the genteel world of antiquities like a new sheriff in town. And for many of the world's top museums, which have long trotted out treasures with dubious origins, his message is simple: this cocktail party is over. Just ask the highbrow crowd at the J. Paul Getty museum, which was finally forced to sign a deal with Rutelli last week to return 40 artifacts that were illegally taken from Italian soil. "This is a fresh start for Getty," Rutelli told TIME. "They are aware that an era is over."

The always suave former Rome mayor made the rounds on Italian national television Thursday night with the first four pieces the Getty has already returned, including a prized 5th century B.C. vase attributed to the Greek painter Euphronios. In an interview this week with TIME, Rutelli said the deal with the Getty — which follows smaller-scale agreements with the Metropolitan Museum of Art in New York and Boston's Museum of Fine Arts — marks a watershed in the international effort to force otherwise upstanding cultural institutions to turn over works with a nefarious past. "We're proud... of the ethical value of this 'cultural diplomacy,'" he said, clearly toning down his tough-guy negotiating posture of recent months, with victory at hand. "In Italy, thanks to this intransigence, illegal digging activity has fallen sharply, and the international accords are blocking much of the trafficking."

Beyond the art thieves linked to established organized crime networks, Rutelli also said there is evidence that terrorists were getting rich off the racket. "There are conversations in which [Sep. 11 suicide bomber] Mohammed Atta was talking about some of the financing of terrorism... coming from the illicit art trafficking market," he said. But Rutelli said there is also a "scientific" motivation for his unprecedented push to resolve these standoffs directly with the musuems. "The issue is also one of context. If you have a stolen masterpiece, you don't know its history. You don't know where it comes from, if it's from Sicly or Apulia, or Magna Grecia," he said. "They are doomed to be anonymous." With that in mind, Rutelli also plays good cop in the negotiations. "To the museum that returns stolen works, we loan for several years works that are equally important and valuable. Therefore, those spaces don't go empty," he said. Indeed, the most precious piece that the Getty has agreed to return — a 5th century B.C. statue of a goddess thought to be Aphrodite — will stay on display at the Los Angeles museum until 2010.

Two issues were not resolved by last week's agreement: the status of the disputed Victorious Youth bronze statue, and criminal proceedings in Italy against Marion True, former curator of the Getty, though a civil suit against True was dropped. The Getty's current Director Michael Brand, who came to the museum in 2005, after it emerged that many items in the collection of the Getty Villa were probably looted from Italian sites, said top museums must help set new tougher standards, though with limits in how far back a country can contest patrimony. He wants to see 1970 as a cutoff date. "Our previous policy was widely acclaimed as one of the strictest in the U.S. It wasn't as strict as the one we have now," he told TIME. "The basic goal is that museums should want to build their collections. But they should also collect responsibly."

For now, it is Rutelli who is doing the collecting. He says once all 40 pieces arrive from Los Angeles, there will be a kind of What-We-Got-Back-From the Getty exhibit. After that, permanent homes will be found, though Rutelli jokes that the statues don't get to choose their company. "After Boston returned her, we sent the statue of the wife of the emperor Hadrian back to Tivoli to be beside her husband, though we're not sure if he was so happy to have her back. He was a restless one." Rutelli, who is happily married, is clearly restless in other ways.