Amy Rigby writes great songs. You might think that’s a basic requirement for any singer-songwriter, but plenty of pro acoustic strummers skate by on pretty vocals or a talent for sustaining an enticing, relaxed mood. Rigby can’t afford such luxuries: she sings in a thin warble, and the mix of humor and pathos in her lyrics is deliberately discomforting. Like most critics’ darlings, she’s got a shtick–she’s the middle-aged single woman who persists in the face of diminishing romantic returns–and on “Rasputin,” the opening track of her fifth album, Little Fugitive (Signature Sounds), she works it as imaginatively as ever, linking her invulnerability with that of the mad monk. Unhappy endings regularly crop up on the album–on “It’s Not Safe” she goes through a bout of postbreakup agoraphobia, and “I Don’t Wanna Talk About Love No More” is self-explanatory. But on the best tracks Rigby picks at the irritating splinters that worry beneath the skin of a relationship. On “The Trouble With Jeanie” she reluctantly makes nice with her husband’s frustratingly likable ex-wife; on “So You Know Now” a guy processes his girlfriend’s promiscuous past amid some Revolver-esque guitar tangles. Rigby and coproducer Jon Graboff choose smart settings for each track here, while, as usual, she uses that frail, wobbly voice to phrase her lyrics with an unlikely precision. In other words, Amy Rigby makes great albums too. David Singer & the Sweet Science open. Sat 10/29, 10 PM, Schubas, 3159 N. Southport, 773-525-2508, $10.