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.