This work considers Cournot-like competition among two public transit oligopolists (a rapid-rail system modeled on the Bay Area's BART, and a parallel bus system) in the presence of a competitively supplied third alternative. The oligopolists compete in both service quality and price, and do so myopically. With demand and cost data from the Bay Area numerically estimated equilibria are obtained and studied. The results indicate that: (1) with fares and product characteristics freely variable, neither mode need operate at a loss; (2) the rapid-rail mode can cover costs from the farebox even if the bus mode offers money-losing service; (3) the equilibria exhibit product differentiation, in sharp contrast to the presently observed situation.