Let [theta](n) denote the maximum likelihood estimator of a vector parameter, based on an i.i.d. sample of size n. The class of estimators [theta](n) + n-1 q([theta](n)), with q running through a class of sufficiently smooth functions, is essentially complete in the following sense: For any...

The asymptotic minimax theorem of LeCam and Hájek is refined by inclusion of terms of order n-1/2. This renders more precise informations about the local properties of superefficient estimator-sequences.