The mechanical timepiece regulator of the invention comprises a flexure bearing oscillator and a double detent escapement, the oscillator comprising a balance wheel (1) connected to an elastic suspension (2a, 2b) arranged to guide and apply a restoring force to the balance wheel (1) in a plane of oscillation. The escapement comprises an escape wheel (3) and an anchor (4) integrated into the balance wheel (1) and having two arms (5, 6) arranged to receive alternately the impulses of the escape wheel (3). The escapement furthermore comprises two detents (7, 8) alternately locking the escape wheel (3) between two impulses and interacting with the arms (5, 6) of the anchor to release the escape wheel (3) before each impulse, without direct interaction between the anchor and the escape wheel.