This revue by writer-director-performer Sandy Hackett, son of Buddy Hackett and longtime friend of Joey Bishop, resurrects the Rat Pack (minus Peter Lawford) with classic bits, topical jokes, and a 12-piece local orchestra. The rehearsed spontaneity is often awkward, but the show swings when the performers sing. Squatty Kenny Jones captures Davis’s side-of-his-mouth style and makes a poignant Mr. Bojangles. Bobby Mayo Jr. lacks Martin’s stature but exudes his tipsy swagger (“That’s Amore” is spot-on). Hackett as Bishop brings to life the stand-up’s sullen drollery but can’t match his extemporaneous savvy. And David De Costa misses Sinatra’s charisma, but if you close your eyes during “My Way” or “Come Fly With Me,” you’d swear Ol’ Blue Eyes was there. Through 5/28: Tue-Fri 8 PM, Sat 3 and 8 PM, Sun 3 PM, Royal George Theatre Center, 1641 N. Halsted, 312-988-9000, $39.50-$69.50.