The capacity allocation problem in a network that is to be shared by noncooperative users is considered, Each user decides independently upon its routing strategy so as to optimize its individual performance objective, The operating points of the network are the Nash equilibria of the underlying routing game, The network designer aims to allocate link capacities, so that the resulting Nash equilibria are efficient, according to some systemwide performance criterion, In general, the solution of such design problems is complex and at times counterintuitive, since adding link capacity might lead to degradation of user performance, For systems of parallel links, we show that such paradoxes do not occur and that the capacity allocation problem has a simple and intuitive optimal solution that coincides with the solution in the single-user case.