(FORTUNE Magazine) – Consultants are almost as popular with organized crime families as they are with corporations. These special counsellors -- lawyers, labor experts, and political advisers -- shuttle between members of the mob and moviemakers, hotel and casino operators, owners of professional sports franchises, corporate chief executives, and public officeholders. They claim to be aboveboard with nothing to hide. But when forced to testify under oath about their underworld connections, they usually become vague. Chicago lawyer Sidney R. Korshak has represented Hilton Hotels Corp., the Los Angeles Dodgers, and numerous other corporations. Nevertheless, former FBI agent William Roemer describes Korshak as ''the most important link between organized crime and legitimate business.'' He has a marvelous ability to help his clients settle labor difficulties. Korshak has always been careful to conceal his organized-crime connections. Investigators learned, however, that in 1958 he helped Tony Accardo draw up a contract that paid the Chicago mob boss $65,000 a year as an employee of a wholesaler called Premium Beer Sales. An FBI bug planted in a mob hangout revealed that Korshak used the code name ''Mr. Lincoln'' in his underworld dealings. Jimmy Fratianno, a gangster-turned-informer, said in his biography The Last Mafioso, that the now-imprisoned former Chicago boss Joe Aiuppa told him: ''Sid is our man,'' adding that he has ''been our man his whole life.'' In 1983 Joseph Hauser, a convicted insurance swindler, testified before a Senate labor investigation that Accardo had told him ''on several occasions (that) he had sent Korshak to Los Angeles to represent the mob there.'' Two years ago Korshak shed a little light on his fixer's role with Hilton. During the hotel's unsuccessful attempt to get a casino license in New Jersey, Chairman Barron Hilton announced that he was dropping Korshak's services because of the Division of Gaming Enforcement's concern about Korshak's underworld connections. The hotel had previously paid him $700,000 in fees. Korshak fired off an angry response to the chairman that was later turned over to the state's gaming investigators: ''I read with interest your disparaging remarks about me,'' he wrote. ''When did you discover that I was associated with characters that shocked your most decent sensibilities?'' Korshak added: ''You will remember calling me in Las Vegas at six one morning while you were with (movie executives) Kirk Kerkorian and Frank Rothman to ask the unions involved not to strike you. As you well know, there was no fee involved.'' Labor consultant Jack McCarthy is still in business even after taking on Rico Construction Co. of Long Island as a client in 1979. Facetiously named after the antiracketeering statute, Rico was an FBI front. In a series of secretly taped conversations, McCarthy agreed to get Rico non-union carpenters for a $5,000 bribe and a promise of future payments. McCarthy had already served time for accepting kickbacks on Teamster pension fund loans and should have suspected that he was being set up. But he did not. Soon he lured Teddy Maritas, boss of the District Council of Carpenters, into the taped conversations. The FBI promptly arrested Maritas and tried him for working with gangsters to rig bids and shake down contractors. The jury was unable to reach a verdict, and Maritas disappeared before he could be retried. Authorities believe he was murdered. McCarthy pleaded guilty to extortion and went to prison again. He was freed in 1982, but is still under close watch. ''We intend to limit history from repeating itself,'' says Ray Maria, deputy inspector general of the Labor Department. In Chicago politics and organized crime have always been linked. The FBI has had Pat Marcy, a 1st Ward Democratic leader, under surveillance since the late 1960s. Former FBI agent Roemer told Senate investigators in 1983, ''Marcy has been calling the shots of the mob as far as politics is concerned for many, many, many years. He was the conduit through which orders of the Outfit passed to those politicians and public officials who were under their control.'' And he still is.