A timepiece includes a mechanical oscillator, formed of a mechanical resonator, and a device for regulating the frequency of the mechanical oscillator. This regulation device includes an auxiliary oscillator, an electromechanical device for stopping the mechanical resonator, a sensor arranged to detect the passage of the mechanical resonator via the neutral position thereof, and a measuring device arranged to measure a time drift of the mechanical oscillator. The regulation device is arranged to stop, during a given alternation, the natural oscillation movement of the mechanical resonator selectively either momentarily during a first half-alternation occurring before the passage of the mechanical resonator via the neutral position thereof when the time drift measured corresponds to at least a certain gain, or prematurely during a second half-alternation occurring after the passage of the mechanical resonator via the neutral position thereof when the time drift measured corresponds to at least a certain loss.