High E string slipping off fretboard
I've got two J customs and both seem to suffer the mild annoyance of the thinnest E string falling off the fretboard without much persuasion. I have a very light touch but even my tapping or legato can push the string off the fretboard now and again.
Has anyone else had this issue with J customs and is there a fix?
Both guitars' necks seem well aligned to me, both Es look equidistant from the fretboard edges, and I doubt both guitars have a wrongly cut nut. This leads me to suspect it is simply the case of the J Custom fret finishing being rounded and not flat to the edge of the fretboard.
Any input appreciated!