We investigate the welfare effect of union activity in a relatively new oligopoly model, the Cournot-Bertrand model, where one firm competes in output (a la Cournot) and the other firm competes in price (a la Bertrand). The Nash equilibrium prices, outputs, and profits are quite diverse in this model, with the competitive advantage going to the Cournot-type competitor. A comparison of the results from the Cournot-Bertrand model with those found in the traditional Cournot and Bertrand models reveals that firms and the union have a different preference ordering over labor market bargaining. These differences help explain why the empirical evidence does not support any one model of union bargaining. We also examine the welfare and policy implications of union activity in a Cournot-Bertrand setting.