The presence of random additive noise is the most important degrading factor in the deconvolution of seismic data. Noise-induced distortion of signal phase and amplitude produces severe stack attenuation, makes poststack recovery difficult with spectral enhancement techniques, and leaves the stratigraphic imprint unclear. The random noise component in the data is estimated from trace segments before the first arrivals and at the bottom of the record beyond seismic basement. An autocorrelation of this noise is used to adjust the signal autocorrelation prior to Wiener-Levinson deconvolution filter design. To improve the robustness of the technique, an iterative surface-consistent wavelet solution (common source, receiver, and offset) is used in preference to a single-channel operation. Use of this deconvolution technique is shown by synthetic and case examples to result in correct phase alignment, enhanced stacking fidelity, and extended signal bandwidth even on very noisy data. The improvement, coupled with sensible handling of coherent noise energy, is crucial for the interpretation of subtle stratigraphic plays in many areas.