Jimmy Page is known to have shaved down is #1 Les Paul neck to be incredibly slim [1]. It make sense because as much as I like Les Pauls, I never really liked the neck profile of mine. It's worth mentioning that there are tons of different neck profiles for Les Pauls throughout the ages, too, so there isn't just one "Les Paul" neck.

[1] https://www.lespaulforum.com/forum/showthread.php?83971-Jimm...