The loss of low-frequency information in reflection seismograms causes serious difficulties when attempting to generate a full-band impedance profile. Information about the low-frequency velocity structure is available from rms (stacking velocities). We show how rms velocities can be inverted with additional point velocity constraints (if they are available) to construct either smooth or blocky velocity structures. Backus-Gilbert averages of the constructed velocity are then autoregressive solutions for recovering a full band reflectivity from band-limited seismograms. Our final result is therefore a full-band acoustic impedance which is consistent with the seismic data section, stacking velocities, and available point constraints.