A simple algorithm is presented for the analysis of transmission spectra provided by a lidar with an emission linewidth that is comparable with or larger than the absorption features of interest. The spreading of line shapes as seen by the lidar precludes use of the classical differential absorption lidar (DIAL) approach. However, it is assumed that, as with the DIAL method, small spectral intervals exist where single absorbers are dominant, and an inversion process for the transmission over such intervals is carried out for the absorber concentration. A second-stage algorithm based on singular-value decomposition is also provided to improve further the concentration estimates. An example situation for use of the algorithms is included wherein the objective is to estimate the concentration of a known trace gas in a composite transmission spectrum in the mid-infrared, where the dominant absorbers are water vapor and methane.