Connors recorded his solo album "Theme to the Guardian" (ECM) in 1974, making the switch from electric to acoustic guitar. Simultaneously he began to study classical guitarists. Two more albums on acoustic guitar followed: "Of Mist and Melting" (1978, ECM) with saxophonist Jan Garbarek, bassist Gary Peacock, and drummer Jack DeJohnette and "Swimming with a Hole in My Body" (1980, ECM). During 1976 and 1977, Connors recorded with Lee Konitz, Paul Bley, and Jimmy Giuffre in New York City. He toured Europe, performing with Luciano Berio and Cathy Berberian. He returned to electric guitar, performing and recording with Garbarek on "Places" (1978) and "Photo with Blue Sky, White Cloud, Wires, Windows and a Red Roof" (1979) and with Tom van der Geld and Richard Jannotta on "Path" (ECM) in 1979. In 1985, Connors recorded "Step It" with Steve Khan on guitar, Tom Kennedy on bass, and Dave Weckl on drums. His next album, "Double Up" (1986), included bassist Kennedy and drummer Kim Plainfield. The same trio (Connors, Kennedy, Plainfield) recorded "Assembler" in 1987.