Elvis Costello, last seen schmoozing on MTV with Tony Bennett, is out to reclaim his turf as the ultimate postpunk balladeer. He goes straight to the sources with Kojak Variety, an album of oldies covers recorded in 1989 before similar ideas were hatched by Annie Lennox and Simon Le Bon. With blues obscurities rubbing up against rock standards, Kojak Variety could have been just another tour of somebody’s impressive record collection. But Kojak is the best album Elvis has released in years, because he never lets himself have such a good time singing his own songs. On R&B singer Little Willie John’s “Leave My Kitten Alone,” he wails about jealousy as if it were fucked-up sexy fun, which for him it is. Kojak’s real stunner is Mose Allison’s “Everybody’s Crying Mercy,” the kind of political broadside Costello has tried to write many times but has always been too wordy to carry...