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We consider the issue of which criteria to use when evaluating the design of a wireless multihop network. It is known, and we illustrate in this paper, that maximizing the total capacity, or transport capacity, leads to gross imbalance and is not suitable. An alternative, which is often used in networking, is to consider the max-min fair allocation of rates, or of transport rates per node. We apply max-min fairness to the class of wireless, multi-hop networks for which the rate of a wireless link is an increasing functions of signal-to-noise ratio. This class includes CDMA and UWB. We show that, for a network in this class, the max-min fair allocation of bit or transport rates always gives the same rate to all flows. We show on one example that such an allocation is highly undesirable when the network is asymmetric. Another form of fairness, utility fairness, does not appear to have the same problem.