We consider the problem of dynamic reorganization of a linear list, where requests for the elements are generated randomly with fixed, unknown probabilities. The objective is to obtain the smallest expected cost per access. It has been shown, that when no a-priori information is given on the reference probabilities, the Counter Scheme (CS) provides an optimal reorganization rule, which applies to {\em all} possible distributions. In this paper we show that for a list of n elements, arbitrary probabilities and any alpha in (0,1), the cost under CS approaches the minimal expected cost up to a ratio of 1 + alpha in O(n lg n alpha^2) reorganization steps.