Paul Schrader took the first phone call at his hotel in New Orleans. It was 1981, and Schrader, who wrote the screenplay for Taxi Driver and went on to direct American Gigolo and other films, was in Louisiana to shoot Cat People, with Nastassja Kin-ski. The woman on the line introduced herself as Miranda Grosvenor, and before Schrader could get rid of her, she had somehow managed to keep him talking for 20 minutes, gossiping about Hollywood and a number of famous men she seemed to know all about.

Intrigued, Schrader invited Miranda to call back, and she did, again and again. “She would just call you up,” says Schrader, “and she was very, very charming. Funny. Sexy. It was incredible. The information she had on people was very accurate. She knew who was where and who was going to do what project. Once that happened, you got into the game, too, because she knew half the dirt on someone, and you added 10 percent. Then she took that 60 percent and went to the next person. . . . And there was always sort of a tease, how good-looking she was, wait till you meet my friends. It was all about talking, flirting, power networking.”

Repeatedly, Schrader arranged hotel-lobby rendezvous with the shadowy Miranda, but she never appeared. Perplexed, he phoned one of the names she had dropped, Michael Apted, director of Coal Miner’s Daughter and Nell. Yes, Apted confirmed, he had talked on the phone with Miranda, too; no, he didn’t know who she was, either. Apted mentioned that Richard Gere had a host of his own Miranda stories to tell. Schrader also reached Buck Henry, the screenwriter and occasional Saturday Night Live host, who confessed he too was captivated by Miranda’s calls, though he also knew her only as a voice over the telephone. Amazed, Schrader nevertheless had neither the time nor the energy to unravel the mystery of his newfound friend. “This went on for five, six months,” he says, “till finally it got so frustrating, all these aborted meetings, I just kind of let it go. I never found out exactly who she was.”

Nor, apparently, did Robert De Niro, who, friends say, also took Miranda Grosvenor’s phone calls. Nor Billy Joel, who tried out songs in progress on her answering machine and considered turning their strange relationship into a musical. Nor Peter Wolf, lead singer of the J. Geils Band, who attempted to meet her at a Louisiana hotel. Nor, in fact, did most of the dozens of well-known and well-to-do men on both coasts who answered calls from Miranda during the 1980s and suddenly found themselves drawn into the most fascinating, invigorating telephone conversations several of them say they ever enjoyed. It wasn’t sex talk, everyone agrees, but it was flirty, gossipy, and more than a little mysterious. “You actually started living for these phone calls,” remembers Brian McNally, the noted Manhattan restaurateur and hotelier. “I was absolutely—I mean, I couldn’t wait for her call. She made you feel fantastic.”

“A lot of nights she was my only friend,” says Joel, who understood that Miranda was also phone pals with Eric Clapton, Steve Winwood, and Sting. “As they say, she did give good phone.”

The story of Miranda Grosvenor, the riddle of who she really was and why she finally disappeared from the phone lines, has grown into a kind of urban legend in certain circles in Los Angeles and New York. The men who talked to her, a number of whom now decline to confirm they did so, came from all walks of the high life; they were actors and directors, rock stars and record producers, athletes and politicians, even a journalist or two. “[I believe] we’re talking about hundreds of people,” says Buck Henry. “This went on for 15 years. There’s lots of people who think they have seen her, and it was not her. We’re talking about someone who can con people into saying they saw her. It’s very complex.”