In late 1960, Gibson changed the body of the whole Les Paul line, adding an upper symmetrical cutaway and doing away with the maple top. The Custom had been working toward thinner necks, and this new model thinned the neck even more, as well as thinning the body while beveling the sides. A plastic Les Paul nameplate positioned between the rhythm pickup and fingerboard. A small pickguard was added to the front of the body in place of the old style floating triangular pickguard.

Les Paul was less than pleased with this new design, and had a falling out with Gibson. He demanded his name be dropped from the guitar line in 1961. Because Gibson had an abundance of plastic Les Paul nameplates, these remained on guitars until the end of 1963. Then, the model changed names to the simple "SG Custom" name.

The SG's thinner body left the neck joint weak. Early models were very prone to neck fractures and breaks at the heel. The neck joint area was thickened in 1962, but this problem would continue to plague the SG for years.