The invention relates to a levelling device comprising a first substantially flat body (1), provided with an appendage (11), in the top part, which has, on a first end, close to the first body (1), a first fracture zone (12) for the separation thereof from the first body (1) and, on a second end, at a distance from the first body (1), a hook (13) for attaching an actuating tool and a second fracture zone (15) with a lower fracture resistance than that of the first fracture zone (12); and a second, upper body (2) containing a passage (21) for mounting said body on the appendage (11) such that it can move into an operative position in which it presses the covering parts (P) against the first body (1).