Standard models of promotion tournaments assume that firms can commit to arbitrary tournament prizes. In this paper, a firm's ability to adjust tournament prizes is constrained by the outside labor market, through the wages other firms are willing to offer to the promoted and unpromoted workers. The paper shows that sufficiently patient firms may be able to retain some control over the tournament prizes through a relational contract, but if the firms are competitive, full efficiency does not obtain in equilibrium even for discount factors arbitrarily close to one. Full efficiency, however, may be feasible in firms with supranormal profits (monopolistic firms). The paper also shows that a minimum wage regulation distorts the workers' investments in human capital by restricting the firms' abilities to design efficient promotion tournaments. A minimum wage thus leads to underinvestment in competitive firms, but could lead to excessive human capital accumulation in monopolistic firms.