John Hammond recording an album of Tom Waits songs produced by Waits would be an ingenious, if suspicious, stroke of cross-marketing if either of them had a market. But Hammond’s new Waits-produced Wicked Grin (Virgin) isn’t exactly Justin Timberlake teaming up with OutKast — which would be a shot as sure as gold chains at a Hip-Hop Hall of Fame awards show. So you can take it on good faith that this collaboration is pretty much what the playas — or, uh, players — involved say it is: a connection between long-time mutual admirers whose paths first crossed back in the ’70s when they appeared as a double bill at a club in Arizona. Hammond headlined.

Hammond, son of the late legendary A&R man John Hammond, has pleased his Muse and paid his bills by paying his dues for almost 40 years, combining flexibility and authenticity in creating a niche for himself as Prince of the Delta Blues. Waits, of course, rode the boxcars of his imagination from the seedy LA motel where he, Rickie Lee Jones, Chuck E. Weiss, and other fellow travelers created a new SoCal bohemian club, adding an artful, emphatic rock-biz layer to the boozy bellicosity of their poet patron saint, Charles Bukowski. Hammond’s relentless touring and recording and single-minded devotion to the blues have afforded him a stature denied to many white blues guys who draw the reverse race card. But he’s never been trendy, and he probably wouldn’t know trendy any more than Carson Daly could identify a John the Conqueror root.

Waits, by contrast, has achieved a steady upward mobility, attaining a Sundance Kid stature in the indie film world thanks to his roles in the films of Jim Jarmusch, and bringing some hipster cachet to the contemporary art-music scene by collaborating with the likes of composer Robert Wilson. The blues have always been the shivs in Waits’s musical tool kit, though since around 1980 his already desperately scorched vocal instrument has sounded more like an audio-vérité recording of a terminal emphysema ward than, say, some sort of slanted, enchanted Howlin’ Wolf homage.

So on Wicked Grin, it’s logical that Hammond — who comes to the House of Blues this Wednesday, sans Waits — would replace Waits’s deranged larynx with his own more efficient, subtle, and well-tuned vox box. And after 40 years of reverence to Muddy, Skip, Elmore, Blind Willie, and the Devil himself, Bobby Johnson, it’s kind of enthralling to hear Hammond sing, play, and think outside his own box, grand as that may be.

It’s said that Hammond and Waits got serious about this project when the bluesman joined the boho on stage two years ago for a version of “Get Behind the Mule,” on Waits’s Mule Variations tour. Which makes sense, since “Get Behind the Mule” is an evocative slog through familiar Delta mud. “Jockey Full of Bourbon” is another standout: Hammond captures the drunken eloquence Waits buried in his own version, a homesick-sounding subterranean pub crawl on 1985’s Rain Dogs (Mercury). Hammond adds a veneer of tenderness, and the organ of Augie Meyers (of the Sir Douglas Quintet and the Texas Tornadoes — and a brilliant musical compadre for Hammond) adds both a soothing texture and a brightening melody.

There’s much more to appreciate from this throbbing symbiosis. “16 Shells from a 30-06” features some of Waits’s most typical yet inspired beat blues hallucinations. Waits’s version, from his 1983 album Swordfishtrombones (Mercury), sounds like Maurice Sendak’s Max: he roars his piteous roars and howls his piteous howls. It’s full of rage, but without street smarts. Hammond kicks it home with the kind of cheer and menace he must have learned by channeling Muddy and Wolf.

The Waits/Hammond dynamics aren’t always so felicitous. Waits and Kathleen Brennan, his wife and long-time collaborator, wrote one new song for the album, “Fannin Street,” whose sentimentality doesn’t fit here. I know what they’re driving at, but the soulful sadness sounds less like Hank Williams than like Andy Williams. Some tunes, like Waits’s now dowdy “Heart Attack and Vine,” are too nonsensical for Hammond’s nuances to achieve anything beyond just hanging around the corner in question. And though Hammond tries to take “Clap Hands” on its own terms, there’s not much for him to scratch beyond the surface: it’s like Captain Beefheart for earthlings, Blue Man Group instead of the blues.

All of which makes you wonder how much Hammond might be able to accomplish if he were set up with another songwriter in need of a singer, a Southerner with a more refined sensibility who also has problems delivering his own oft-great but increasingly erratic material. If they haven’t yet met, someone should introduce John Hammond to Randy Newman.

John Hammond plays the House of Blues this Wednesday, April 4. Call 497-2229.