In an unregulated electricity generation market, the degree to which generators in different locations compete with one another will be greatly determined by the capacity of transmission lines. We show, however, that there may be no relationship between the effect of a transmission line in spurring competition and the actual electricity that flows on the line in equilibrium. We also demonstrate that limited transmission capacity can give a firm the incentive to restrict its output in order to congest transmission into its area of dominance. As a result, relatively small investments in transmission may yield surprisingly large payoffs in terms of increased competition. When applied to a model of California's deregulated electricity market, the analysis indicates that at least one firm could have an incentive to strategically induce transmission congestion and that the payoff to expanding transmission capacity could be quite high even though the additional capacity would seldom be used in equilibrium.