From the introduction: ``\n M. A. Girshick et al.\en [Ann. Math. Statist. {\bf 17} (1946), 13--23; MR0019897 (8,477d)] have studied the problem of the unique unbiased estimator (i.e., MVUE) of the fraction defective, $p$, in a sequence of binomial trials under different stopping rules. Some of the stopping rules described in their paper [op.\ cit.] resemble the curtailed single and double attribute sampling plans. \n A. C. Nelson, Jr.\en, \n J. S. Williams\en and \n N. T. Fletcher\en [Technometrics {\bf 5} (1963), no. 4, 459--468] have compared four experimental procedures for estimating the probability, $p$, that a defective item fails in a field test. Their second procedure is equivalent to the semicurtailed single sampling plan. They have given an approximate expression for the variance of the MVUE of $p$ under this experimental procedure. In this paper we study the problem of the variance of the MVUE of the fraction defective, $p$, under a fully-curtailed single sampling plan. We observe that the direct evaluation of the variance of the MVUE is not simple. Hence we give bounds for the variance of the MVUE. The bounds for the variance of the MVUE in the case of a semicurtailed single sampling plan can be derived in a similar way and are given without details. It is observed that the lower bound is greater than the Cramér\mhy Rao lower bound. The bounds given are very easily evaluated using standard binomial tables.''