  In order to optimize the directed motion of an inertial Brownian motor, we
identify the operating conditions that both maximize the motor current and
minimize its dispersion. Extensive numerical simulation of an inertial rocked
ratchet displays that two quantifiers, namely the energetic efficiency and the
P\'eclet number (or equivalently the Fano factor), suffice to determine the
regimes of optimal transport. The effective diffusion of this rocked inertial
Brownian motor can be expressed as a generalized fluctuation theorem of the
Green -- Kubo type.
  Addendum and Erratum
  The expression for the effective diffusion of an inertial, periodically
driven Brownian particle in an asymmetric, periodic potential is compared with
the step number diffusion which is extracted from the corresponding coarse
grained hopping process specifying the number of covered spatial periods within
each temporal period. The two expressions are typically different and involve
the correlations between the number of hops.
