  We show how the resummation of large logarithms can be incorporated into the
method of effective charges. As an example, we apply this approach to the event
shape variables thrust and heavy jet mass in e+e- annihilation. We find that,
although the resummation creates problems with the behaviour of the efective
charge in the 2-jet limit, smaller power corrections are required to fit the
data compared to the standard approach. In addition, increasing the logarithmic
accuracy reduces the size of the power corrections further. We also consider
``predicting'' the sub-leading logarithms in the MSbar scheme, obtaining
surprisingly good results for the first few NLL terms.
