The traditional model of collective bargaining confines unions to settlements constrained by the employer's labor demand curve, but an alternative model places wage-employment outcomes on a contract curve that extends beyond the labor demand curve. This paper derives a multidimensional (hedonic) contract-curve model in which employment-security provisions are used to maintain efficient bargains outside the employer's demand curve and distinguishes empirically between the contract-curve and demand-constraint models using data for public school teachers in New York State. Estimates clearly support the contract-curve model over the demand-constraint model by linking the gap between compensation and the value of the marginal product to the strength of employment-security provisions.