SUMMARY Two criteria are set up to judge the relative performance of the least squares estimator and the best linear unbiased estimator of , in the linear model y = X/, + u, where E(u) = 0, E(uu') = F. The matrices X and r are found so that the relative performance of least squares is worst. Both criteria give the same least favourable situation: when X(X) is any one of the 2k manifolds (Y1 +? Yn, ***., Yk ? Yn-k+l), where Fyi = fiyi andf1 < ... < fn are fixed, ,/(. ) denoting the subspace spanned by the columns of the relevant matrix. The case where allfi may be chosen in a preassigned interval is also discussed. The practical implications of the various results are mentioned.