This Monte-Carlo study compared modified Newton (NW), expectation-maximization algorithm (EM), and minimum Cramer-von Mises distance (MD), used to estimate parameters of univariate mixtures of two components. Data sets were fixed at size 160 and manipulated by mean separation, variance ratio, component proportion, and non-normality. Results indicate that NW is the poorer estimation procedure. EM is less sensitive to different initial inputs and produced the lowest singularity rate. MD is more robust to non-normality and to incorrect model assumption of variance. In practice, MD is recommended. The singularity problem is not severe enough to be a practical concern. (Twelve figures present details of the simulations and analyses.) (Author/SLD)