The Π method for estimating an underlying smooth function ofMvariables, (xl, …,xm), using noisy data is based on approximating it by a sum of products of the form Πmφm(xm). The problem is then reduced to estimating the univariate functions in the products. A convergent algorithm is described. The method keeps tight control on the degrees of freedom used in the fit. Many examples are given. The quality of fit given by the Π method is excellent. Usually, only a few products are enough to fit even fairly complicated functions. The coding into products of univariate functions allows a relatively understandable interpretation of the multivariate fit.