  The motion of self-propelled particles can be rectified by asymmetric or
ratchet-like periodic patterns in space. Here we show that a non-zero average
drift can already be induced in a periodic potential with symmetric barriers
when the self-propulsion velocity is also symmetric and periodically modulated
but phase-shifted against the potential. In the adiabatic limit of slow
rotational diffusion we determine the mean drift analytically and discuss the
influence of temperature. In the presence of asymmetric barriers modulating the
self-propulsion can largely enhance the mean drift or even reverse it.
