In 1969, Beckett and his fellow players David Hood, Roger Hawkins and Jimmy Johnson broke away from Fame and opened their own Muscle Shoals Sound Studios in Sheffield, Alabama, with financial assistance from Jerry Wexler of Atlantic Records. Beckett began to amass some memorable credits as both musician and, increasingly, producer. His first production effort was a collaboration with Hawkins, and it generated the minor Mel & Tim classic Starting All Over Again (1971). Meanwhile he made memorable contributions to a string of recordings with the Staples Singers, the hard rocker Bob Seger – including his hit albums Night Moves (1976) and Stranger in Town (1978) – Linda Ronstadt, Boz Scaggs, JJ Cale and Leon Russell.
It was Russell who gave the studio band the nickname the Swampers, which was memorialised in Lynyrd Skynyrd’s hit Sweet Home Alabama, and three Swampers (Beckett included) appeared with an expanded line-up of the British rock band Traffic on their 1973 live album On the Road. When Paul Simon travelled down to Alabama looking for some of that Muscle Shoals lustre, Beckett and friends played on his hits Kodachrome and Loves Me Like a Rock in 1973, and later on Still Crazy After All These Years (1975).