  Consider a graph G with an assignment of costs to vertices. Even if G and all
its subgraphs admit balanced separators of sublinear size, G may only admit a
balanced separator of sublinear cost after deleting a small set Z of
exceptional vertices. We improve the bound on |Z| from O(log |V(G)|) to O(log
log...log |V(G)|), for any fixed number of iterations of the logarithm.
