Water-layer multiples and peg-legs are a frequently occurring problem in marine data processing. For data from areas with slow lateral variations and moderate amplitude of the water-bottom reflection, these reverberations can often be suppressed by predictive deconvolution. However, when the sea bottom is hard, the traditional approach usually disappoints. Moreover, irregularities of the sea floor and departures of the subwater structure from the supposed 1-D earth model invalidate the traditional approach even when the sea-floor reflection is moderate.