The essential elements of practical nonlinear least squares analysis of atmospheric absorption spectra are discussed. These include speed of analysis, flexibility of spectrum type, and stability in the presence of noise. A computer program which embodies these elements is described, and two types of results are presented. The first is a series of least squares analyses of synthetic spectra, both noise free and noisy. The second is a summary of results from analyses of high resolution solar spectra. Among the parameters which have been fit are trace gas mixing ratios, temperatures, spectral background, instrument resolution, phase error and channel spectrum parameters, line shifts, intensities, and broadening coefficients.