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This paper examines the problem of recovering the acoustic impedance from band-limited normal incidence reflection seismograms. Recognizing the inherent nonuniqueness in the inversion, we proceed by constructing an impedance model which satisfies the processed seismogram, has a minimum of structural variation, honors any point impedance constraints that are provided, and incorporates information from stacking velocities. The constrained inversion is carried out in a single operation using linear programming methods. The constructed impedance is consistent with available geological and geophysical information and therefore constitutes a well-constrained estimate of the true earth impedance. A basic assumption in our inversion is that each seismic trace is a band-limited representation of the true reflectivity function. When seismic data do not conform with this assumption, pre-inversion processing of the data is required; this involves a series of data checks and possible corrections. A complete processing sequence incorporating all steps of the practical inversion is presented and illustrated with field data examples.