If nothing else, Elvis Costello deserves thanks for doing what many Allen Toussaint fans have wanted to do for years. For The River in Reverse, he rummaged through Toussaint’s voluminous song catalogue for unjustly overlooked gems, in the process confirming the suspicions of Toussaint’s fans who have waited very patiently for him to revisit some of those songs. Costello and Toussaint demonstrate how commercially and artistically powerful those songs are, and some though some gain resonance for the album’s proximity to the flooding that followed Hurricane Katrina — “Nearer to You,” for example — but it shouldn’t have taken a natural disaster to get Toussaint to break out “Tears, Tears and More Tears” and “Wonder Woman.”

That’s a minor benefit, though. If all the album did was tell us something we already knew, it would be a pleasant footnote to Toussaint’s career. Costello and Toussaint wrote new songs and retrofitted old ones to address Katrina and its aftermath, making a powerful album that capitalizes on the power of association. “Nearer to You,” for example, wasn’t written as a hurricane song, but phrases such as “Every little thing I do / I’m trying to get closer to you” and “I’ve got to get nearer / nearer to you” emerge from the lyric. Those lines literalize the song, so instead of being one about a guy trying to connect to the woman he loves, it becomes one about a man struggling to reach his loved one.

Similarly, in “Freedom for the Stallion,” Costello sings, “Lord, have mercy what you’re going to do / about the people who’re praying to you / they’ve got men making laws / destroy other men / they’ve made money / god, it’s a doggone sin / Oh Lord, you’ve got to help us find a way.” That passage jumps out of the song and captures the sense of helplessness and injustice, looking for help while feeling abandoned or abused by all the higher powers.

In the Costello-penned title track, a different but related strategy emerges. Far less direct a writer than Toussaint — the product of a different era and songwriting aesthetic — the song is an apocalyptic dreamscape dominated by images of water and destruction. When he finally sings, “What do we have to do / to get this river in reverse?” the river could be water, politicians, or any number of things that seem to have gone down a very wrong path.

Whatever the case, there’s no avoiding the emotional impact of the line and the one before it: “I don’t think that it can get worse.”

Costello projects may invite a lit-conscious approach, but The River in Reverse is hardly a trip to the library. Much of it rocks, powered by Costello’s band, the Imposters, and augmented by Toussaint’s Crescent City Horns.

“Ascension Day” is “Tipitina” played in a minor key, and “Tears, Tears and More Tears” is defined by the rousing horn fanfare behind the title phrase in the chorus. “Who’s Gonna Help Brother Get Further?” may deliver the album’s ray of hope, but it also features some of the liveliest playing. Steve Nieve plays his B3 as if he’s trying to trump all New Orleans’ great organ players in one 5-minute song, and “Big Sam” Sammie Williams’ verse-long trombone solo grabs listeners’ attention before the track returns to the chorus.

The River in Reverse was recorded here at Piety Street Studios last December while the emotional wounds from Katrina were still pretty fresh, but by dealing with the hurricane through a series of musical sideswipes and allusions, Costello and Toussaint made an album that doesn’t require Katrina to make sense, though it’s far more resonant when though thought of in the storm’s context.