The Billie Holiday classic “God Bless the Child” has inspired so many singers to trample over this wounded reflection on poverty, need and the humiliation of the have-nots that it was a shock to hear it persuasively delivered on Tuesday evening at Cafe Carlyle by the offspring of Hollywood royalty. That would be Rumer Willis , the 27-year-old daughter of Bruce Willis and Demi Moore, who refrained from the style of declamation that many pop singers nowadays adopt to demonstrate a bogus empathy. With an excellent band led by her musical director and pianist James Sampliner, Ms. Willis dug into its hurt feelings and made you feel that this child of privilege has known more than her share of woe.

Ms. Willis is already something of a celebrity, having won the 20th season of “Dancing With the Stars” and gone on to play Roxie Hart in the Broadway revival of “Chicago.” Nightclub singers generally fall into two types: those who study a song and figure out an interpretation, which they superimpose; and those who instinctively dive into the lyrics and live inside them, without overthinking. Ms. Willis belongs to the second group; in other words, she’s a natural.

Her voice is strong with a wailing upper register that she wielded with an awareness of how far to go before reaching a point of diminishing returns. The more conflicted and tougher the song, the more deeply Ms. Willis appeared to relate to it. She made you feel the self-administered whiplashes in Amy Winehouse’s “You Know I’m No Good,” the rage in the Pat Benatar hit “Bloodshot Eyes” and the guilt in Fiona Apple’s “Criminal.” At the same time, she didn’t overdo it.

The collective experiences of the songs she chose describe a sensitive young woman who has been so emotionally abused by her peers in the dating pool that she has turned to older men. It came to a head with a strong rendition of the Brandi Carlile hit “The Story,” whose lonely narrator has a wealth of experiences behind her but no one to share them with.