Most Bayesian clean speech estimators, like the Wiener filter or Ephraim and Malah's amplitude estimators, are derived under the assumption that the true power spectral density (PSD) of speech is known. In practice, however, only estimates are available. When the PSD estimation errors are neglected, they propagate through to the final speech estimate, resulting in undesired artifacts such as musical noise and speech distortions. To increase the robustness to PSD estimation errors, recently a linear estimator has been proposed that explicitly takes into account the uncertainty of the available speech PSD estimate. In this paper, we show that in the derivation of this estimator a limiting statistical assumption is made, and that avoiding this assumption leads to a novel, potentially more powerful nonlinear estimator under PSD uncertainty. In combination with a sophisticated speech PSD estimator, the proposed approach achieves a higher predicted speech quality than the linear alternative and its conventional counterpart, the Wiener filter.