If Nelson Algren had written material for a lounge act, and the lounge was a riverfront dive on some peculiarly American tributary of the Styx, the result might have resembled a show by Tom Waits, who gave the first of six concerts at the Eugene O'Neill Theater on Broadway on Tuesday.
The vivid, deftly realized characters in Mr. Waits's songs stumble down back streets and alleys, pursued by demons, clutching a crumpled hat, an old accordion, a tattered dream. They're doomed, but indomitable; as long as they've got friends, and the bars are open, they can look forward to an eternity of torment and be almost cheerful about it.
Most of the songs in Mr. Waits's show are drawn from ''Swordfishtrombones,'' ''Rain Dogs'' and ''Franks Wild Years.'' On these recent albums, Mr. Waits outgrew the hipster poses and ''Beautiful Losers'' romanticism of his earlier work. His lyrics got tighter and cut closer to the bone. The music, plundered from the scrapheap of Saturday-night Americana, filled in color and detail with painterly strokes.
At the Tuesday night show, Mr. Waits's musicians wrenched lounge-act cliches and other musical detritus out of their original contexts and cobbled them into extravagant, exquisitely ramshackle structures.
Ralph Carney's imaginatively off-center saxophone lines lurched along, mocking the liquid grace of Willy Schwarz's accordion and keyboards. Marc Ribot's recombinant guitar stylings cooked blues, country, punk and jazz down to molten slag. Greg Cohen, a bassist, and Michael Blair, a drummer, were equally idiosyncratic and equally solid. At times, their music simulated chaos, but it was a meticulous, structured chaos, full of surprises and beyond category as we know it.
Mr. Waits's voice still sounds like the hoarse rasp of a terminal tobacco fiend, but it's a musical rasp. His singing is confident and richly textured, with admirable phrasing and intonation. And Mr. Waits is still punctuating his singing with outlandish body English - scuttling sideways like a down-and-out crab, creeping, lurking, pouncing.
Dissecting Mr. Waits's music may facilitate analysis, but it's misleading. He used to be a mannered, eclectic performer whose artifice constantly threatened to subsume his art. He has become an authentic original whose work coheres into a satisfying whole.