Mick Jagger, 58, has taken a big step in his relationship — if you want to call it that — with L’Wren Scott, 35. The Rolling Stone is having the floors in his London flat lowered 10 inches to give his 6-foot 2-inch — or is it 6-foot 4-inch? — model-turned-stylist girlfriend, who has been hitting her head on the apartment ceilings, a little more headroom. Plans for the renovations have been approved by the local council and are about to begin, in spite of the fact that Mick’s ex-wife, Jerry Hall, claims that this thing he has with L’Wren is not a good influence on their four children, Elizabeth, James, Georgia May and Gabriel, who live with their mother in the house next door. What, the kids like short people?

Cornelia Guest is back from her Los Angeles stay, where the darling girl is working on film projects to oversee the 100th Anniversary of the Humane Society at the Robert Miller Gallery, which she is co-chairing with Adrien Brody Thursday evening. After the society’s photograph auction, she’ll nip down to SoHo to the opening of Links of London’s new outpost, where she’ll design herself a one-of-a-kind charm bracelet from the world’s first ever “Charm Bar.”

Early in the day, Cornelia will perch in the front row of Lana Marks’ spring show, featuring her Cleopatra evening clutches as well as her alligator jet totes, which you will be thrilled to hear Sarah Jessica Parker totes hither and thither in baby blue. Others expected are Deeda Blair, Sharon Bush and Lorraine Bracco. The show supports the Blue Harbor Foundation, which funds research for bipolar disorder.

This story first appeared in the October 13, 2004 issue of WWD. Subscribe Today.

Cornelia will stay in town just long enough to attend the opening of the Duchess of Marlborough’s exhibit of her paintings on Tuesday at Lars Bolander’s gallery in the Meatpacking District before returning to the West Coast. The next time that you see Cornelia will be on the silver screen. Oh goody!

Jude Law and Sienna Miller want to set the record straight about their romance and their future plans. They are “madly in love” but are being sensible about it. They say that recent reports of their engagement are “complete nonsense.” But Sienna does add, “He’s a great guy. I’m lucky.” No arguments there.

Had enough of Gwynny and Chris? Well anyhow, they’re looking for a nanny for their little girl, Apple, as both their careers are keeping them busy. This comes as a surprise — not really — to some of her friends, since she has so adamantly censured working mothers for not spending enough time with their children. Gwyneth was quoted just a few months ago as saying, “I might not work for ages. Acting is a great job, but it is not going to define my life.” Apparently Gwyneth has passed the point of no return.

But how could she resist playing Marlene Dietrich and Peggy Lee, both of whom she is signed to portray in upcoming movies? By the way, it is now being whispered by her new neighbors in London that the house she bought from Kate Winslet and Sam Mendes is haunted. I thought you’d want to know, particularly if anyone out there was thinking of applying for the position of Apple’s nanny.

Trying to keep one’s head above water in the New York social swim is not for the faint of heart. So you wonder why there are so many brave souls out there valiantly breasting the current every night. Good for them. You do realize, don’t you, that they are all swimming upstream? Well of course. Who in society wants to go in the other direction? It’s the season when nobody stays home, so the only way to track them down is chronologically, as in better late than never.

Ahmet Ertegun — you can easily call him a towering figure in the music world, what with his Atlantic Records and all that jazz — and his chic wife, Mica, celebrated the opening of the Ertegun Jazz Hall of Fame, which they named in honor of Neshui Ertegun, Ahmet’s late brother and partner, in the new home of Jazz at Lincoln Center, the Frederick P. Rose Hall. All very black tie.

An international panel voted such jazz greats into the inaugural hall as Art Tatum, John Coltrane, Billie Holiday, Coleman Hawkins, Dizzy Gillespie, Jelly Roll Morton, Duke Ellington, Miles Davis, Louis Armstrong, Lester Young, Sidney Bechet and Charlie Parker.

Among the Erteguns’ chums taking in all that you know what were Lisa Schiff, chairman of Jazz at Lincoln Center, Mercedes and Sid Bass, Nancy Kissinger, Oscar and Annette de la Renta, Antoinette Guerrini-Maraldi and Wynton Marsalis, the Jazz at Lincoln Centers’ artistic director. All those cats up in heaven would have loved it.

Scattered around the rooms: Nan Kempner, fancy hostess, fancy dresser, and server of some of the fanciest food in town, tip-to-toe in a Calvin Klein white silk blouse and balloon-y felt pants; Joan Collins, there with her husband, Percy Gibson, in a fetching dress that slipped off her shoulders because it was supposed to; Louise Grunwald; Anne and Jim Sitrick; Duane Hampton; Judy and Sam Peabody; Sally and Rufus Albemarle; Tina and James Givenchy; Bobby Short; Caroline Roehm; Cathy Bryant; Mary McFadden; Carol and George McFadden; Peter Bacanovic, and the guest of honor, Jill Cartter.

On Friday, read about the glittering gala opening of Carnegie Hall with a brilliant audience of swells and an even more brilliant performance by the Philadelphia Orchestra.

Also, all about the parties for Bob Colacello of Vanity Fair who, after six years, has just finished his marvelous book, “Ronnie and Nancy,” about the Reagans. Is it definitive? More than that even.

And, last but not least, the wedding party given by new bride Hilary Geary, now Hilary Ross, and billionaire steel and textiles man Wilbur Ross, who were married in Southampton last Sunday. They celebrated Monday night with a huge party at the Rainbow Room.