Provision of a tolled road can yield profit and welfare increments that have opposite signs. This can arise directly from government subsidy or from inability to make full use of price discrimination. But this paper analyses indirect effects that arise from network interdependence. Examination of simple network models shows how such divergence can occur. In particular, if profitability of a new, tolled link depends on extraction of user surpluses previously enjoyed on the earlier network, addition of the new link can be welfare-negative. Thus the profit test cannot displace cost-benefit analysis.