Segmented mold for molding and vulcanizing a tire of given diameter (DS), having a width (L) and a diameter (J) at the interconnect point (E), comprising shells and segments collaborating to withstand the internal pressure and remain in the closed position without assistance from additional components, in which mold each segment comprises at its lateral edges a projection extending radially inwards, which projection is equipped with a lip extending axially towards the inside of the mold and having an inclined frustoconical surface of given angle (α) with respect to the axis (XX′) of the mold such that the extensions of the line of each frustoconical surface on a meridian plane intercept on the radially internal side of the segment concerned, and in which mold each shell comprises a projection extending radially outwards and provided with a lip having a frustoconical surface inclined by the same angle α with respect to the axis XX′ of the mold. The distance (α) comprised between a straight line (tt′) parallel to the axis of the mold and passing through the point (T) of application of the resultant of the forces (F) of contact between the shells and the segments, and a straight line (ss′) parallel to the axis of the mold situated in the extension of the internal face of the resistant segment is equal to k * 0.42 * D s ⁡ ( L J ) 2 , with a coefficient k comprised between 0.8 and 1.4.