Generalized linear inversion is applied to synthetic and real seismic data sets with the objective of obtaining an impedance profile as a function of time. The impedances solved for are parameterized in a manner that describes the unknown earth using fewer variables that previous seismic generalized linear inversion techniques. Single traces of common-midpoint (CMP) processed data will be inverted. The method of generalized linear inversion (GLI) presented here is designed to improve on recursive inversion with respect to relative and absolute scale of the impedance results, resolution of impedance boundaries, and distortion from residual wavelet effects. Other advantageous aspects of GLI are insensitive to noise in many cases, and it will allow an interpreter to fix the impedance of any number of known lithologies in an interval being inverted. This last property is extremely useful when evaluating a prospect on an otherwise well-understood seismic line.--Modified journal abstract.