Conventional marine seismic data is affected by the interference from ghosts on both the source and receiver sides. The natural diversity provided by propagation directions, depth variations and imperfect reflections at the sea surface means the notches are not as deep as they often appear after stack. For a flat streamer, the apparent time delay between the main signal and its ghost is angle dependent, and deterministic de-ghosting in the τ-p domain can reduce the effect of ghosts and retrieve the original wavelet spectrum. For a linearly-slanting streamer, further to the angle-dependant time shift a lateral separation occurs in the angle dimension. The amplitude and phase discrepancies around the notch frequencies caused by the variations in depths and effective refection coefficients can be reduced by using a stochastic search for the optimum set of de-ghosting parameters. A deconvolution process stabilized by averaging over a large number of traces in common–slowness panels may be used to address the remaining spectral defects.