  We study coherent backscattering of a quasi-monochromatic laser by a dilute
gas of cold two-level atoms. We consider the perturbative regime of weak
intensities, where nonlinear effects arise from {\em inelastic} two-photon
scattering processes. Here, coherent backscattering can be formed by
interference between {\em three} different scattering amplitudes. Consequently,
if elastically scattered photons are filtered out from the photodetection
signal by means of suitable frequency-selective detection, we find the
nonlinear backscattering enhancement factor to exceed the linear barrier two.
