Singer Bettye LaVette is finding a devoted following among a new generation of fans.

There are musicians who cover songs — and then there is Bettye LaVette. Whether the 65-year-old singer is performing Fiona Apple or Pink Floyd, she owns it completely, altering the lyrics and melody to suit her perspective. From LaVette, interpretation is the highest form of flattery.

LaVette has been called a soul singer, but she has little use for the term — which she dismisses as a “white euphemism.”

“I’ve never heard any of us refer to each other as soul singers,” she says, preferring instead to be called a rhythm and blues singer. “No matter what genre a song comes from, when I sing it, it will be rhythm and blues.”

Over the past few years, LaVette has transformed songs by Aimee Mann, Dolly Parton, Led Zeppelin and many others into her trademark sound. Most famously, she performed a powerful version of the Who’s “Love Reign O’er Me” at the Kennedy Center Honors in 2008, which reportedly brought Who vocalist Roger Daltrey and guitarist Pete Townshend to tears.

Not too long ago, LaVette would have thought such a moment impossible. She began singing professionally as a teen in the early 1960s, scoring a hit with “My Man — He’s a Lovin’ Man” and touring with James Brown and Otis Redding.

The next 30 years were a struggle for the singer, but she is finally receiving the acclaim her voice deserves. “Most of me had given up on that,” she says of finally breaking through. “But I guess a part of me didn’t, because I kept working out and keeping my voice strong.”

LaVette has recorded three albums in the past six years, sealing her comeback and introducing herself to a new generation of fans. She’s now working on a memoir with writer David Ritz and choosing songs for her next record of interpretations. The selection process, she explains, is crucial.

A good song “has to make a lot of sense,” she says, “because I do look my audience in the eye. After that, it doesn’t take too much to make them my own. It’s me that sings them, and I don’t know how to sound like anybody else.”

Atlas Theater, 1333 H St. NE; Sat., 8 p.m., $40; 202-399-7993. (Union Station)