A timepiece has a basic movement including at least one barrel (12) and a set of hands (14) for displaying the time now, the set of hands being situated at a first level, a mechanism for a supplementary function connected to at least one hand (18a) for displaying the supplementary function, the hand being situated at a second level and on a different axis from the set of hands (14), and an automatic winding mechanism for the barrel (12), including an oscillating mass (24) consisting of a carrier (24a) and a heavy sector (24b) situated at the periphery of the carrier. The carrier (24a) pivots in a plane situated between the first and second levels.