It is shown that the BAN (best asymptotically normal) estimates of μ the mean and σ the standard deviation of normal populations based on incomplete (singly or doubly truncated) samples of sizenare asymptotically jointly less efficient than the corresponding estimates based on complete samples of the same size. The joint efficiency,eT(xα,xβ), of the estimates based on incomplete samples is seen to be a monotonic function of the points of truncationxαandxβ(xα<xβ). A table ofeT(xα,xβ) for several given values of the points of truncation is presented.