  The contribution of the two-step process gamma + d -> p + n -> pi0 + d to the
imaginary part of the amplitude for coherent pion production on the deuteron is
calculated exploiting unitarity constraints. The result shows that this
absorptive process is not negligible and has to be considered in an extraction
of the elementary neutron production amplitude from the gamma + d -> pi0 + d
cross section at threshold. In addition, it is argued that a consistent
calculation of gamma + d -> pi0 + d in baryon chiral perturbation theory beyond
next-to-leading order requires the inclusion of this absorptive process.
