A mainstay on Congress Avenue since 1991, the Elephant Room is one of Austin’s most important music venues. The long and narrow basement room is the Live Music Capital’s hub for local jazz players, who bring top-notch musicianship to the club seven nights a week.

When longtime fixture Stanley Smith left Austin in 2018 after more than a quarter-century of Tuesday happy-hour gigs at the Elephant, singer and songwriter Sarah Sharp got the nod to take that slot. Working with a band that includes world-class guitarist Mitch Watkins, Sharp has made Tuesdays an ideal after-work stop for the downtown crowd.

With an atmosphere that’s unlike any other music room in town, the Elephant has lots of quirks, from the dollar bills (many with notes or messages written on them) stapled to the ceiling to the cool-and-dark feel of its underground space. And then there’s the ceiling beam adorned with the tombstone-ish phrase “The Remains of Tony Campise,” a tribute to the late, celebrated saxophonist who was an Elephant regular for two decades.

Before she took over the 6 p.m. Tuesday show, Sharp had played here many times with Jitterbug Vipers, a self-described “swingadelic” outfit featuring the husband-wife team of guitarist Slim Richey and bassist Francie Meaux Jeaux. Their drummer, Masumi Jones, also plays with Sharp at her Tuesday residency. On bass most weeks is Pat Harris; when we attended her show on HAAM Day last week, Chris Maresh was filling in.

Watkins, a former member of Leonard Cohen’s touring band who also holds town a Thursday residency at the Elephant, first played with Sharp a few years ago at a C-Boy’s gig in which they happened to be opening for Leon Bridges, just before he became nationally known. Sharp had first connected with Watkins about 15 years earlier, when she sent him some demo recordings and boldly predicted, “I really feel at some point we’re going to work together.”

Their styles complement each other at the Elephant. Sharp is an enchanting vocalist, with an upper register that can dish out sweet and sassy tones in equal measure. On Tuesdays, they’ll play some of her own songs — she released several EPs last year — alongside tunes you probably know well. But you probably haven’t heard them sound quite like they do in the hands of Sharp and her bandmates.

“We cover things you wouldn’t have thought of, and we cover them in really different ways,” she says. Their take on "Blue Eyes Crying in the Rain" is mesmerizingly beautiful; a jaunty choice to end the first set last week was "Sunny Side of the Street," while on other evenings we've reveled in their slow-burn rendition of "Oh, What a Beautiful Morning" from "Oklahoma."

Watkins has seen far more than his share of stages both big and small, but these Tuesdays with Sharp’s band are something he clearly enjoys. “There’s real communication on this gig — unspoken communication, all the time,” he says. “It’s pretty much like nothing I’ve ever experienced.”

Sharp recently made a record with Yaniel Matos, a Cuban musician who lives in Brazil, that hasn’t yet been released, and she’s been writing new material with Watkins and other Austin collaborators. Some of the fresh stuff gets an airing on Tuesdays. “We try the new things at the very beginning, before the room has filled up,” she says.

As with most weekly residencies in Austin, this isn’t a gig that requires rehearsal. In many respects, such residencies are rehearsals unto themselves. The musical repertoire develops and evolves over time simply by being played week after week onstage.

“Mitch has said to me many times, ‘My week starts on Tuesday,’” Sharp says. “We come here to play for each other, and with each other. We love being in the moment of the actual music.”

The venue: Tables and chairs stretch from the front door at the bottom of the stairs to the edge of the stage on the other end of the long-rectangle room. Grab a spot up close if you’re there for the music, or sit alongside the classic wooden bar, one of the best and longest in town. The sound system is simple but usually sounds good, in part because the musicians who play there tend to be regulars who’ve come to know its quirks well.

If you go: Sharp and her band play two sets from 6 p.m. to 8 p.m., with a break of around 15-20 minutes between. Admission is free; there’s a tip jar up front if you like what you hear, and Sharp usually has copies of her records on hand for sale. Parking can be tricky downtown, though sometimes street spots open up as office workers head home. A handful of pay lots and garages are within a few blocks. Tuesday music at the Elephant pairs well with downtown dining at locations such as Swift’s Attic, directly upstairs from the venue, or across-the-street standbys Manuel’s and Second Bar & Kitchen.

OTHER RECENTLY FEATURED RESIDENCIES:

Steel guitar takes the spotlight on Mondays at Sam's Town Point

Casper Rawls, Thursday early-evenings at Continental Club

Margaret Wright, happy hour Thursday-Friday at Skylark Lounge

Resentments, Sunday evenings at Saxon Pub

Butter N Jam, Wednesday nights at Dozen Street

Bluegrass Night, Monday at Radio Coffee & Beer