An underdamped rocked ratchet operated at very low temperatures and damping is shown: (i) to be capable of rectifying the ac input signal more efficiently than in the overdamped regime; (ii) to be insensitive to the initial conditions, at variance with noiseless, or deterministic, ratchets; and (iii) to be characterized by a wide damping "window," where its efficiency is appreciable also for weak input amplitudes. All these properties are rather robust, irrespective of the wave form of the drive and the ratchet potential. Our results relate to recent experiments on current-biased annular Josephson junctions and also on rectifiers of magnetic flux quanta in superconductors.