Presents the effects of the predictive filtering of waveform data in multiple passes as the first stage of a two-stage lossless compression algorithm. Predictive compression has a proven track record when applied to high dynamic range waveform data, wherein the waveform data are input to a linear predictor or perhaps an adaptive predictor for decorrelation, and the resultant residue is then subjected to an entropy coder to (ideally) represent the signal with a minimum number of bits. This compression is commonly applied with no loss of information. In this work, an adaptive filter is used for prediction, but instead of a single run through the predictor, the residue is continually passed back through the predictor in an attempt to further decorrelate the residue. Multiple passes of a gradient adaptive lattice filter has given the best decorrelation, yielding improved compression ratios. We run the compression technique on a seismic database, then provide some comparative lossless compression results using several coding schemes and show that using multiple-pass predictive filtering can improve the compression rates attainable.