“Someday they’re gonna write a blues song just for fighters,” said the heavyweight champion Sonny Liston, who would meet his own bad end. “It’ll be for slow guitar, soft trumpet, and a bell.” Cat Power’s Chan Marshall opens her new album, “The Greatest” (Matador), with just such a song. A version of it anyway, this one for brushed electric guitar, “Moon River” strings, and piano.

The title track tells the story of a fighter once possessed of high hopes and physical power: “Once I wanted to be the greatest,” Marshall sings, lovingly licking the words, “two fists of solid rock / with brains that could explain any feeling.” The song could be about Jack Johnson, or Joe Louis, or Liston himself. All we know is that like them, this once great fighter ends in ruin: “Then came the rush of the flood / stars of night turned me to dust.”

The elegiac quality recalls a song from Cat Power’s last album, “I Don’t Blame You,” about Kurt Cobain or someone an awful lot like him. It followed the same trajectory, from admiration bordering on awe to tragedy. But “The Greatest” is a far more fully realized song, and with poetry such as “Melt me down to big black armor / leave no trace of grace, just in your honor,” she surpasses her previous efforts. In this way, the new album title is apt. In every respect Marshall deepens and expands her past work; this is her superlative effort.

Early in her career – which began in 1995 with the album “Dear Sir” – her voice had a quality of damaged blankness. Everything sounded as if it was sung from a fetal position (a pose she even assumed on stage sometimes). But on “The Greatest” her voice has a sturdy thickness about it. It doubles and triples upon itself. She’s become her own support group.

The arrangements have grown to match. Marshall used to wrap all her songs in the same threadbare comfort blanket of amateurish, minor-key guitar. It was a spare indie rock sound, very much in line with early Liz Phair. But here we find Marshall embracing her inner Norah Jones. The album drips with the warm sounds of ’70s Memphis soul, reproduced here by Al Green’s guitarist and songwriting partner Mabon “Teenie” Hodges and an assortment of journeymen Memphis musicians.

Marshall is famous (or notorious, depending on who you ask) for her emotional insecurity and onstage breakdowns. For fans it’s the root of her charm. This album retains plenty of that trademark fragility amid a newfound confidence and teasing selfawareness. On “Hate” she sings conspiratorially, “Hey come here, let me whisper in your ear / I hate myself and I want to die.” Then, feigning shock on behalf of the listener, she asks,”Do you believe she said that? Can you believe she repeated that?”

“Empty Shell” addresses the same former lover as “Good Woman,” another song from the last album. Both pair simple electric guitar with plaintive country fiddle. “I don’t want to be a bad woman / and I can’t stand to see you be a bad man / and this is why I am leaving,” she explained on the latter; now she’s healed and offers this advice to the man: “When she sits on your lap / try to pretend to laugh / when she does stupid things / just like I used to do / do not hate her,” she cautions, “for to leave her is to love her the same as you and I.”

The best songs, however, are less confessional, and sound like they were written anywhere but in her personal journal. “Lived in Bars,” a lush blues, opens with a metronomic piano and sour, mute-muffled horn. The lyrics are a lovely metaphor for I’m not sure what: “Swords and arches, bones and cement / light in the dark of the innocent of man,” she sings. Then, two minutes or so in,the tempo doubles and the dreamy imagery takes flight: “Lived in bars and danced on tables / hotel’s drains and ships that sail / swim with sharks and fly aeroplanes out of here / out of here.”

Shoo dop, shoo dop, shoo dop. She’s no longer shadow boxing. Now she’s punching above her weight.