Les Paul mentioned in one of his bios that he envisioned the guitar that eventually carried his name to incorporate a neck-thru-body design. His prototype was something along the lines of a 4X4 whittled down with the sides glued onto it. Gibson thought this design would be too costly to manufacture and went with the set-neck design used today.

Probably Gibson's Firebird should rightfully carry the Les Paul name, because it is closer in design to how Les envisioned "his" guitar.