  As a first step in the project of ratchet optimisation, the optimal driving
waveform among a wide class of admissible functions for an overdamped,
adiabatic rocking ratchet is shown to be dichotomous. `Optimum' is defined as
that which achieves the maximum (or minimum negative) average particle
velocity. Implications for the design of ratchets, for example in
nanotechnological transport, may follow. The main result is applicable to a
general class of adiabatic responses.
