Given an undirected graph G ( V , E ) , a set of traffic matrices H and one additional traffic matrix h , we say that H totally dominates h if, for each capacity reservation u supporting H , u also supports h using the same routing pattern. It has been shown that if | H | = 1 ( H = { h ˆ } , say) and G is a complete graph, H totally dominates h if, and only if, h ˆ ≥ h component-wise. In this paper we give a generalized condition for | H | ≥ 1 and any undirected graph.