I pulled Bentley's "Costumes by Karinska" off the shelf and the layering of colors pherank describes was used by Karinska elsewhere and earlier, including in Cotillon. Bentley says Bérard's maquettes were lovely but also rather general (even if more specific than other sketches Karinska worked from), and it was Karinska who added many of the details and grace notes of the costumes in her execution of them. From the book:
Bentley reproduces the well-known photo of a wistful young Toumanova in her Cotillon costume; it was Bérard who asked for something sparkly on the skirt, but Karinska who came up with little moons, stars, and musical notes. Ultimately, the costumes of Cotillon incorporated "sea green, lemon, cyclamen, rose, and lime."
Bentley reproduces a cool group photo taken in Monte Carlo in the early thirties, with Karinska, Youskevitch, Massine, Markova, Bérard, and Kochno; Bérard is bearded and hearty, with a hand on Kochno's shoulder.
If you take a good look at the "white" costumes for the Rosenkavalier section of "Vienna Waltzes" you'll see a lot of off-white.