The overlap function of a Raman channel for a lidar system is retrieved by nonlinear regression using an analytic description of the optical system and a simple model for the extinction profile, constrained by aerosol optical thickness. Considering simulated data, the scheme is successful even where the aerosol profile deviates significantly from the simple model assumed. Application to real data is found to reduce by a factor of 1.4-2.0 the root-mean-square difference between the attenuated backscatter coefficient as measured by the calibrated instrument and a commercial instrument.