A tire (10) for driving on ice, comprising: a tread (20) having a rolling surface configured to come into contact with the ground when the tire is rolling along, and two lateral faces (27), this tread comprising at least one groove (25, 26) in the rolling surface; at least one stud (30) having a longitudinal axis (33), a part (31) of the stud projecting from the rolling surface, the intersection between the stud and the plane tangential to the portion of the rolling surface around the stud forming a contour C, that part of the stud that projects from the rolling surface having a minimum cross section Sm, Sm corresponding to the smallest cross section of the said part in any plane containing the radial direction that passes through the point of intersection between the longitudinal axis of the stud and the plane tangential to the portion of the rolling surface around the stud; at least one conduit (200-205) that forms, on the rolling surface of the tire, at least two opposing edges (211, 221; 212, 222; 213, 223), the minimum distance D between the conduit and the contour C being less than or equal to 1 cm, the conduit opening into the groove and/or onto a lateral face of the tread; wherein, for each stud, the sum of the mean cross sections Sn of the conduits, each mean cross section Sn being measured at right angles to one of the opposing edges formed by the conduit, is greater than or equal to half the minimum cross section Sm of that part of the stud that projects from the tread.