Vulcanizing device with radially mobile segments comprising: a bottom plate supporting a bottom shell for molding a tire sidewall, an axially mobile top plate supporting a top shell for molding a tire sidewall, an axially mobile closure ring comprising an inclined interior face, a plurality of circumferentially arranged adjacent segments of which the interior radial faces comprise linings for molding the tread of the tire and of which the inclined exterior radial faces are able to collaborate with: first means of coupling with the closure ring which are produced in such a way that the axial movements of the closure ring involve a radial movement of the segments, and second means of coupling the segments to the top plate which are able to connect the segments to the top plate and to allow their radial movement, the said second means of coupling being adjustable on the circumference of the top plate.