A new method for detecting spikes in acoustic Doppler velocimeter data sequences is suggested. The method combines three concepts: (1) that differentiation enhances the high frequency portion of a signal, (2) that the expected maximum of a random series is given by the Universal threshold, and (3) that good data cluster in a dense cloud in phase space or Poincaré maps. These concepts are used to construct an ellipsoid in three-dimensional phase space, then points lying outside the ellipsoid are designated as spikes. The new method is shown to have superior performance to various other methods and it has the added advantage that it requires no parameters. Several methods for replacing sequences of spurious data are presented. A polynomial fitted to good data on either side of the spike event, then interpolated across the event, is preferred by the authors.