Consider a distribution function F in the domain of attraction of an extreme value distribution G_β with unknown extreme value index  . An appealing nonparametric estimate of β is the Pickands estimator  , which is based on the 4m largest observations in a sample of size n generated independently according to F. If F satisfies a von Mises condition with rapidly decreasing remainder term, we can establish asymptotic normality of convex combinations   of Pickands estimate. With the asymptotically optimal p = p_opt∈[0,1] minimizing the limiting variance of   Pickands estimator   is then clearly outperformed by the convex combination  . As popt depends on β, a data-driven version   is plugged into  , with the resulting estimate being asymptotically as good as  . Simulations demonstrate the superiority of the convex combination   over the Pickands estimate already for moderate sample sizes n.