Levelling a fretless board is an exacting task - even small variations can case nasty buzzes. With the strings off, get the neck as flat as possible using the truss rod. Remove the nut. Then use a truly flat sanding beam the length of the fingerboard until the board is truly flat end to end. Refinish the board and reinstall the nut. You will need to lower the nut slots to account for the amount of wood you removed from the board.
Hello!
Thanks for advice!
It seems I have to leave the "lady" to a pro, then.
I've very much figured out how to do it, the same way you describe it, but was hoping to avoid removing the nut, but I belive you've right. The nut has to come off, to reach sanding the part of the fretboard nearest the nut.