The method of moments is employed with “single” truncated random samples; (1) to estimate the mean,μ, and the standard deviation, σ, of a Pearson Type III population when α3is known; and (2) to estimateμ, σ, and α3when only the form of the distribution is known in advance. No information is assumed to be available about the number of variates in the omitted portion of the sample. The results obtained can be readily applied to practical problems with the aid of “Salvosa's Tables of Pearson's Type III Function.” An illustrative example is included in the paper.