  We present the first calculation of coherent backscattering with inelastic
scattering by saturated atoms. We consider the scattering of a
quasi-monochromatic laser pulse by two distant atoms in free space. By
restricting ourselves to scattering of two photons, we employ a perturbative
approach, valid up to second order in the incident laser intensity. The
backscattering enhancement factor is found to be smaller than two (after
excluding single scattering), indicating a loss of coherence between the doubly
scattered light emitted by both atoms. Since the undetected photon carries
information about the path of the detected photon, the coherence loss can be
explained by a which-path argument, in analogy with a double-slit experiment.
