In this paper we present a solution to the nonlinear spectral estimation problem for speech enhancement. We start from a rather simple statistical model (log-normal) for the short time spectral estimates of speech and noise. By empirical data generation and curve fitting approaches we are able to get explicit, though simple, expressions for the MMSE estimator in function of input level and the model parameters for each frequency component. The great advantage of our approach is that it has a sound theoretical foundation, is general by the choice of its parameters, and almost as simple to use as classical spectral subtraction. Moreover, using a neural network as function approximator, which is found to be the best for our curve fitting problem, other model based MMSE estimators can be readily implemented with the proposed approach.