Lee Konitz on the Miles Davis' "Birth of the Cool":
Miles was the titular leader because he had more of a name, and I suppose he could get the gigs; big deal, so he got one week at the Royal Roost. [...] The (Birth of the Cool) nonet was an arranger's band, because they rehearsed the music. Miles made some suggestions, but very few that I recall; I thought of it as Gerry's [Mulligan] band really. The nonet was a chamber ensemble where the solos were incidental to the writing, which was the most important aspect. - Fifties Jazz Talk: An Oral Retrospective, by Gordon Jack
In the early 1990s Mulligan decided to revisit his work with the Birth of the Cool band; he felt that a lot of the arrangements were done in a haste and wanted to do them justice.
In 1992, Mr. Mulligan revisited the "cool school" that began with the Birth of the Cool recording and assembled the Gerry Mulligan Tentet. The project, entitled "Re-Birth of the Cool" began with a recording for the GRP label with Mulligan, and Wallace Roney in Miles Davis's trumpet chair.
In the summer of 1991, in Rotterdam, Gerry told Miles he was planning to play the music again. Miles was very enthusiastic and said to let him know when it was going to be. Sadly, it was not to be, as Miles passed away.
The Gerry Mulligan Tentet, the Re-Birth of the Cool touring band, featuring Art Farmer on flugelhorn/trumpet and Lee Konitz on alto sax, embarked on a highly successful concert tour. - Bio
Click to read a good review by Eric Thacker from The Essential Jazz Records: Modernism to postmodernism.
Gerry Mulligan - Re-Birth Of The Cool 
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11. Darn That Dream