  The optical conductivity of a d-CDW conductor is calculated for electrons on
a square lattice and a nearest-neighbor charge-charge interaction using the
lowest-order conserving approximation. The spectral properties of the
Drude-like peak at low frequencies and the broad hump due to transitions across
the gap at large frequencies are discussed, also as a function of temperature
and of the second-nearest neighbor hopping term t'. We find that vertex
corrections enhance the d.c. conductivity, make the Drude peak narrower and
provide a smooth transition from a renormalized regime at low to the bare
theory at high frequencies. It is also shown that vertex corrections enhance
the temperature dependence of the restricted optical sum leading to a
non-negligible violation of the sum rule in the d-CDW state.
