It’s taken far too long for someone to get around to paying tribute to Rosemary Clooney. Surprisingly (in a good way), that someone turned out to be Bette Midler. Safely sidestepping anything that might smack of jazz, the Divine Miss M. stays focused on the mid-’50s hitmaker Clooney throughout Bette Midler Sings the Rosemary Clooney Songbook (Columbia). Fortunately, several of Clooney’s signature tunes-“Hey There,” “Tenderly,” “You’ll Never Know,” “In the Cool, Cool, Cool of the Evening”-also happen to be terrific songs. Reuniting with former accompanist Barry Manilow (who, literally he claims, dreamed up the idea and coproduced the album with Robbie Buchanan) has done Midler a world of good. In recent interviews she’s conceded that for once she abandoned her control freakishness and let Manilow run the show. Wise decision. Gone is all the scenery-chewing, Streisandesque grandiosity. In its place is a refreshingly muted Midler who comes remarkably close to approximating Clooney’s distinctive phrasing and inimitable sincerity. We’ll forgive her getting overly rambunctious (sounding suddenly like Bette ‘N the Hood) on the goofy “Mambo Italiano,” especially since her “Memories of You” is so softly reverential and her sugary duet with Linda Ronstadt on “Sisters” is so relentlessly adorable.