A timepiece regulating mechanism with a magnetic escapement, including transmission train, a magnetic escape wheel set, a resonator wheel set, a return means, said regulating mechanism including an energy storage means arranged to deliver energy in the form of an output torque, via said transmission train, to said magnetic escape wheel set, forming a magnetic escapement mechanism with said resonator wheel set subjected to the torque from said return means, said magnetic escape wheel set cooperating with said resonator wheel set, either directly, or via a magnetic stop member comprised in that case in said regulating mechanism, said magnetic escapement mechanism being arranged to operate when said magnetic wheel set receives a torque higher than or equal to a maintenance torque specific to said magnetic escapement mechanism, wherein said transmission train includes a torque regulating means arranged to deliver to said magnetic escape wheel set a constant torque comprised between 1.0 and 2.0 times said maintenance torque, said torque regulating means including a fusee of continuously variable cross-section from which unwinds a chain wound by a drum driven by said energy storage means.