A South Austin church recently converted into a part-time music venue might not have seemed an obvious setting for a great show from Rickie Lee Jones, whose live performances have at times vacillated with the circumstances. “I guess I can tell you now, I really thought this show was going to suck,” she confided at the end of a two-hour concert at the 04 Center that was, instead, a joyously wondrous evening with one of America’s greatest living singer-songwriters.

Mixing material from an intriguing new covers album called “Kicks” with beloved tunes from her 40-year career, Jones enchanted an audience with a repertoire that was remarkably diverse in sound and style. Moving from acoustic guitar to electric guitar to piano — and even working in a brief swing on snare drum in the finale — Jones consistently made magic with her three-piece band that the audience dearly appreciated.

Partial standing ovations arose repeatedly from the full house of about 300, and the warm reception clearly inspired Jones. “Thank you for hooting and howling and clapping really loudly,” she said at one point, just before launching into “We Belong Together,” one of several songs from the 1981 classic album “Pirates” that mesmerized the crowd.

When they weren’t applauding and cheering her on, the crowd was pin-drop quiet for more hushed numbers that sounded great in the A-Frame-styled venue with a high ceiling. Seating at the 04 Center is comfortable, with reasonable leg room; there’s a full bar in the lobby, though a long line pre-show indicated they might need to find space for a second bar stand. A spacious parking lot out front filled completely but appeared to be just enough to accommodate almost all attendees.

Jones seemed won over by the vibe in the venue early on, giving sometimes extended and often fascinating introductions to several songs. (A particularly good one involved a memory of driving down Sunset Boulevard with Little Feat’s Lowell George and admiring the Chateau Marmont hotel, where Jones later lived for a stretch.) She’ll turn 65 later this year, but Jones seems to have lost nothing of her spectactular, instantly recognizable voice; those high flights on songs such as “Chuck E.’s in Love” and “The Last Chance Texaco” were still as magnificent as they sound on record.

The crowd also embraced the material she played from the new album, which ranged from the more bluesy “Bad Company” (by the 1970s band of the same name) to Steve Miller’s “Quicksilver Girl” to the show-closing Mills Brothers gem “Nagasaki.” Throughout, she got perfect support from a versatile three-piece ensemble, with Mike Dillon on drums, percussion and vibes at stage right while Cliff Hines and Robbie Mangano switched between, guitars, bass, keys and mandolin as well as adding essential backing vocals.

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