This paper reviews fast iterative reweighted least squares (IRLS) and residual steepest descent (RSD) algorithms for L
p,

, deconvolution. The timing aspects and the implementation of the IRLS algorithm on an array processor are discussed. The effectiveness of L
1deconvolution and its insensitivity to noise bursts are illustrated using simgle synthetic as well as complex seismic data. Finally, it is shown that the L
pprediction filters are stable as long as

.