Russell Smith, the lead singer, songwriter and rhythm guitarist for the country-rock band the Amazing Rhythm Aces, died on July 12 in Franklin, Tenn. He was 70.

The cause was complications of cancer, his longtime bandmate Jeff (Stick) Davis said.

Mr. Smith’s smoky, coarse-timbred baritone was heard on the Amazing Rhythm Aces’ biggest hits, including 1975’s gospel-themed “Amazing Grace (Used to Be Her Favorite Song),” the group’s sole Top 10 country hit. “The End Is Not in Sight (The Cowboy Tune),” a soulful number written by Mr. Smith, earned the band a Grammy Award for best country vocal performance by a duo or group the next year.

His most enduring original was “Third Rate Romance,” a droll yet tender song about a one-night stand that has been recorded by artists ranging from Elvis Costello and Rosanne Cash to the proto-new wave band the Fabulous Poodles.

“I called my mama when I first wrote that song and I played a little of it on the telephone to her,” Mr. Smith recalled in an interview published on classicbands.com. “I called her and said, ‘Mama, I think I’ve written a hit song.’