(FORTUNE Magazine) – CHIEF EXECUTIVES on lobbying missions are almost as common as tourists on Capitol Hill. Effective ones are a lot rarer. Here is a list of the best of the bunch, based on interviews with dozens of legislative aides and business lobbyists: Robert Beck, 60, of Prudential, who is also chairman of the Business Roundtable, wins the prize for persistence. ''He's here on everything from health to taxes,'' says a Senate Finance Committee aide. ''He trusts the legislative system.'' The staffer says Beck is popular on the Hill because of his lack of arrogance. Beck says he loves making the trip from his Newark, New Jersey, headquarters because Washington is ''the town where things happen.'' The mutual admiration paid off in provisions of the Deficit Reduction Act of 1984, which changed taxation methods in ways that were beneficial for life insurance companies like Prudential. James D. Robinson III, 50, of American Express and Finn Caspersen, 44, of Beneficial Corp. are known as aggressive lobbyists and good salesmen. Robinson is said to have ''moxie,'' and Caspersen is famous for knowing his stuff. Both have fended off attempts by commercial banks to encroach on their industries. J. Peter Grace, 72, flamboyant chairman of W.R. Grace who headed the President's commission on cost cutting in government, is admired for the force of his personality. ''He's combative, persuasive, and lots of fun at the witness table,'' says a Senate staffer. Corporate raiders Carl Icahn, 50, and T. Boone Pickens, 57, are popular too. ''They don't come off at all as hard- nosed or bullies,'' says a top Senate aide. Icahn is diplomatic and cooperative. Pickens, says another aide, is an ''exceptionally good listener.'' Stephen Levy, 45, chairman of Bolt Beranek & Newman, a Cambridge, Massachusetts, high-tech company, and of the American Electronics Association, impresses House staffers with, as one puts it, ''facts, not rhetoric.'' On a recent visit Levy called on his Congressman, who happens to be House Speaker Thomas P. ''Tip'' O'Neill. Staffers say that as Levy laid out his industry's trade problems, O'Neill took notes. Later that afternoon O'Neill told aides he wanted a bill out of the House by May 15 to stiffen U.S. trade rules. Robert Mosbacher, 59, chairman of Mosbacher Energy, an oil and gas company in Houston, works the Administration as well as Congress. He helped run Treasury Secretary James Baker's campaign for Texas attorney general in 1978. Friends in the Senate include oil patch lawmakers like Russell Long of Louisiana and Lloyd Bentsen of Texas. ''The door is always open for Mosbacher,'' marvels a business lobbyist, ''He has incredible access.'' The most successful lobbying chief executives understand the town's backslapping, go-along, get-along ways. For their part, legislators are impressed when corporate chieftains, rather than hired lobbying guns, come calling. Says a business lobbyist: ''Legislators know that the commitment of a professional lobbyist to an issue is only as deep as his current client's.'' Chief executives take heed.

CHART: NAME COMPANY REPUTATION ON THE HILL Robert Beck Prudential Trusts the legislative system. James D. Robinson III American Express Has clout; good salesman. Finn Caspersen Beneficial Accessible; knows his facts. J. Peter Grace W.R. Grace Fun at the witness table. Carl Icahn TWA Cooperative; diplomatic. T. Boone Pickens Mesa Petroleum Good listener; no gunslinger. Stephen Levy Bolt Beranek & Newman Armed with facts not rhetoric. Robert Mosbacher Mosbacher Energy Close friends in high places.