Jolie Holland didn’t come from out of nowhere, she just sounded that way. The Texas-raised singer-songwriter had already been a founding member of the Vancouver, B.C., old-timey band the Be Good Tanyas before she moved to San Francisco and started making some lovely, low-budget recordings that would eventually be released in 2003 as the album Catalpa. The songs were recorded largely in her apartment, probably around the kitchen table, with just her simple guitar accompaniment and maybe a friend playing banjo here and there as Holland’s voice swoops up to and down from and in between notes, playing with syllables like Play-Doh.

Catalpa came across as a folk artifact — something wonderful that accidentally got recorded and released. Of course, it wasn’t accidental; Holland knew just what she was doing. And her ambitions, both artistic and commercial, have grown steadily since then. Holland’s new single, “Mexico City,” sounds like a play for a bigger audience: It’s almost like one of those Americana songs they fawn over on NPR.

Don’t get me wrong: It may not be a bad idea to tighten up Holland’s arrangements and rein in some of her more self-indulgent tendencies, but she’s never going to be a conventional artist — and I don’t think anyone should try to make her one. That fact may be best illustrated by Holland’s cover of “Pure Imagination,” the syrupy theme from the old Willy Wonka movie, which she recorded for a children’s album. Her version sounds less like chocolate than bourbon and cough syrup. In fact, it’s more appropriate to the weirdness of the movie than Gene Wilder’s original version was. It’s perfect.

JOLIE HOLLAND, Belly Up, Sunday, October 12, 9 p.m. 858-481-8140. $15.