Marking his first foray into film tunes, Michael Mills — bassist for alternative rockers R.E.M. — has inked a deal with 20th Century Fox to compose the score for Fox 2000′s upcoming pic “A Cool, Dry Place.” R.E.M. will write and record one new song for the film’s soundtrack.The deal marks the first time Mills and the group have agreed to develop a score and original song for a feature film, although their songs have been used in several film soundtracks. Mills was said to have expressed interest in the film after reading Michael Grant Jaffe’s novel “Dance Real Slow,” on which the film is based. After meeting with helmer John Smith to discuss ideas for the score, Mills then signed on as composer. Currently lensing in Toronto, the 1998 release stars Vince Vaughn, Joey Lauren Adams and Monica Potter. Katie Jacobs and Gail Mutrux are producing Matthew McDuffie’s adaptation. “Cool, Dry” tells the story of a young attorney (Vaughn) who, after his wife (Potter) leaves him and their young son, moves back to his Midwest roots and struggles with single fatherhood. He finds romance with a local woman (Adams), but complications arise when the boy’s mother comes to reclaim her son. Most successful bands One of rock’s most successful bands, last year R.E.M. signed a landmark five-album, $80 million contract with Warner Bros. records — one of the richest deals ever struck in the music industry. The band released its latest album, “New Adventures in Hi-Fi” — its final album under its previous deal with Warner Bros. and the band’s 10th full-length album overall — in September. Mills is not the first of the Athens, Georgia-based quartet who has felt the lure of Hollywood. Michael Stipe, the band’s lead singer, founded Single Cell Pictures, which has a production deal with New Line Cinema. Fox currently is in negotiations with distributors for the soundtrack.