Rabbitt signed with Elektra Records in 1975. His first single under that label, "You Get to Me", made the top 40 that year, and two songs in 1975, "Forgive and Forget" and "I Should Have Married You", nearly made the top 10. These three songs, along with a recording of "Pure Love", were included on Rabbitt's 1975 self-named debut album. In 1976, his critically acclaimed album "Rocky Mountain Music" was released, which included Rabbitt's first number-one country hit, "Drinkin' My Baby (Off My Mind)". In 1977, his third album, "Rabbitt", was released, and made the top five on Country Albums chart. Also in 1977, the Academy of Country Music named Rabbitt "Top New Male Vocalist of the Year". By that time, he had a good reputation in Nashville, and was being compared by critics to singer Kris Kristofferson. In 1977, at Knott's Berry Farm, Rabbitt appeared at the Country Music Awards and sang several of his songs from "Rocky Mountain Music". He won the Top New Male Vocalist of the Year award.