The pristine and lightly quavering sound of Kate McGarry’s voice doesn’t send up any flares identifying her as a jazz singer. But she certainly deserves the designation, as she confirmed with a well-rounded performance at the Jazz Standard on Thursday night.

Ms. McGarry is appearing at the club this week with most of the musicians heard on “The Target,” her third release on Palmetto and, by all measures, her best. In the half-dozen songs from the album that figured into Thursday’s second set, she showcased a few bright facets of her style: poetic introspection, rhythmic brio and a willingness to be swept along by her ensemble’s undertow.

On “Do Something,” one of several prewar standards front-loaded in the set, Ms. McGarry explored a variable approach to phrasing over a smooth but lively background provided by the Hammond B-3 organist Gary Versace, the bassist Matt Penman and the drummer Clarence Penn. The assertive swing of the arrangement vaguely evoked Betty Carter, who memorably recorded the tune. Ms. McGarry even scatted a bit — a dangerous idea when the ghost of Ms. Carter is in the room — and managed to push through, if not prevail.

Ms. McGarry gets a lot of mileage out of more contemporary material, including what might be categorized as nostalgic middlebrow pop. Her last album was named “Mercy Streets,” after a Peter Gabriel song; “The Target” accommodates something by Sting. But in their live incarnations, “Sister Moon” (the Sting tune) and “Chelsea Morning” (a Joni Mitchell classic) were effective improvisational vehicles for Ms. McGarry as well as Mr. Versace, on piano and accordion, and Donny McCaslin, on tenor saxophone.

A tantalizing flicker of Ms. McGarry’s lyrical ability surfaced in a fine rendition of the Miles Davis ballad “Blue in Green.” The song’s deceptively simple melody proposes something like an endless loop, with each phrase drifting up into the next. Ms. McGarry’s lyrics make the most of that feeling. She accomplished something similar, though a bit more precious, with the words she wrote to “She Always Will,” written by the guitarist Steve Cardenas, a former member of her band.

Ms. McGarry’s guitarist at the Jazz Standard, Keith Ganz, is also her husband. He played thoughtfully throughout the set, but his most notable contribution was an original tune, “New Love Song,” that he and Ms. McGarry performed as an acoustic duet. The lyrics, by Ms. McGarry, strike a self-referential and mock-apologetic note: I’m sorry for bothering you with this hackneyed sentimentality, but I can’t help myself.