Allen Toussaint experienced a late-career revival sparked, ironically enough, by the devastation of Hurricane Katrina in 2005. He had to leave his hometown New Orleans after the hurricane, relocating to New York City where he started to play regular gigs at Joe’s Pub and, soon enough, he cut The River in Reverse with Elvis Costello. That 2006 album propelled Toussaint toward a greater audience, leading to more headlining concerts, two of which are chronicled on Rounder’s 2013 release Songbook. Recorded in 2009 at Joe’s Pub, Songbook features nothing more than Toussaint alone at a piano running through songs he’s written over the decades. He sprinkles in a New Orleans standard here and there — there’s an excellent rendition of “St. James Infirmary” — but the spotlight is on his peerless originals, songs that are standards in their own right: “Lipstick Traces (On a Cigarette),” “Holy Cow,” “Get Out of My Life, Woman,” “Yes We Can,” a medley of “A Certain Girl/Mother-in-Law/Fortune Teller,” “Southern Nights.” Toussaint’s voice sounds smooth and silky — he in no way seems as if he’s in his seventies — and his piano is similarly nimble as it glides from signature New Orleans stride and boogie to sophisticated, elegiac chords. Perhaps this album packs no revelations — there are no rearrangements, nothing unexpected in the songs — but as an elegant summation of strengths, this Songbook is mighty attractive.