This article proposes a very tractable approach to estimating parameters for mixtures of normal distributions. The analyst proceeds as if, in addition to the data, he or she had observed some pseudo data points drawn from each distribution whose values reflect his or her priors. The approach eliminates the singularities associated with maximum likelihood estimation and offer guidance for choosing among alternative local maximum likelihood estimates. Monte Carlo analysis established its consistent potential to improve mean squared errors. Data sets on which maximum likelihood estimation has presented difficulties are shown to be readily analyzed with the quasi-Bayesian procedure.