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In a quest for a generic unbiased scatterometer wind inversion method, the different inversion procedures currently in use are revisited in this paper. A careful examination of both the errors in the wind and in the measurement domain, combined with the nonlinear shape of the geophysical model function (GMF), leads to a generic and novel Bayesian wind retrieval approach in the measurement domain. In this approach the shape of the GMF solution manifold in measurement space is more important than the specified noise. This shape is related to the system wind direction sensitivity, and when this sensitivity is uniform, realistic and precise wind direction distributions are retrieved, even when measurements lie far from the GMF manifold. A simplified measurement space transformation that produces such uniform sensitivity for the European Remote Sensing Satellite (ERS) scatterometer is presented and shown to have reduced wind direction bias compared to the more traditional (measurement-noise normalized) inversion for ERS. Moreover, the simplified wind inversion reveals a similar performance to the current operational ERS wind inversion, but is potentially more generally applicable. The simplified method is then applied to SeaWinds but is ineffective. In this case the instrument geometry results in a low sensitivity to wind direction at a few specific directions. As a consequence, certain wind direction solutions remain favored in the SeaWinds inversion.