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The usual inversion procedures for determining the oceanic circulation take the density field as given. This does not explicitly account for the mismatch between the data, which are typically a single realization of the density field, and the circulation being estimated, which may be a time mean or some other smoothed quantity, but explicit consideration of the uncertainty of the density data renders the problem nonlinear, and new estimation methods have to be used. As an example, a nonlinear inversion is successfully applied here to the simple analytical model of Stommel and Veronis (1981). It is also shown that their linear procedure, if properly used, yields a much better result than they obtained.