Abstract This note illustrates the application of the Λ-minimax principle (see, e.g., [6, Sect. 6.6]) to the estimation of a scale parameter. In particular, σ Λ-minimax estimator of the variance of a normal distribution is obtained when Λ is a subset of the class of natural conjugate prior distributions. Two cases considered are (1) the mean is known and (2) a fully specified prior distribution is available for the mean. Case 2 is reduced to Case 1.