A tread (1) for a tire with a preferred rolling direction, the tread having grooves (2) of substantially circumferential orientation which delimit ribs (30, 31, 32, 33, 35), at least one of which is provided close to each of its traverse edges with a plurality of incisions of width smaller than 1.5 mm. The incisions open onto the contact surface of the tread, are essentially parallel to one another, and having a mean inclination α different from zero relative to the direction perpendicular to the rolling surface (S) of the tread. The tread is characterized in that, when viewed in a section plane perpendicular to the rotational axis of the tire, each incision in a given rib, relative to a perpendicular to the contact surface of the rib at the point where the incision intersects the surface, has an inclination which varies through the thickness of the tread, each incision being inclined at an angle β1 relative to said perpendicular at its point of intersection with the rolling surface when new, the angle β1 being larger than the angle α, and at an angle β2 at the point of the incision furthest inside the tread, the angle β2 being smaller than the angle α. The point of the incision furthest inside the tread being located, relative to said perpendicular, such that it is ahead of the point of the incision located on the contact surface of the rib.