Recent studies of DSDP samples from layer 2A of oceanic basement have found complex magnetic stratigraphies that seem incompatible with the frequent existence of linear short-wavelength anomalies caused by palaeomagnetic field behavior. Statistical models are developed for the lateral variation of the average magnetization of layer 2A: a Poisson series for reversals of the earth's field and a stairstep random series for discrete magnetic units. It is shown with the power-density spectra of these statistical models that lateral inhomogeneities must average out over distances of less than a few hundred meters. Specifically, individual magnetic units of the type seen at DSDP Site 332 cannot extend uniformly for distances greater than a few hundred meters. ?? 1979.