We propose a method of estimating mixing distributions using maximum likelihood over the class of arbitrary mixtures of Gaussians subject to the constraint that the component variances be greater than or equal to some minimum valueh. This approach can lead to estimates of many shapes, with smoothness controlled by parameterh. We show that the resulting estimate will always be a finite mixture of Gaussians, each having varianceh. The nonparametric maximum likelihood estimate can be viewed as a special case, withh= 0. The method can be extended to estimate multivariate mixing distributions. Examples and the results of a simulation study are presented.