The paper proposes a model of on-the-job search and industry dynamics in which search is directed. Firms permanently di er in productivity levels, their production function features constant returns to scale, and search costs are convex in search intensity. Wages are determined in a competitive manner, as rms advertise wage contracts (expected discounted incomes) so as to balance wage costs and search costs (queue length). Firms are assumed to sort out their coordination problems with their employees in such a way that the on-the-job search behavior of workers maximizes the match surplus. Our model has several novel features. First, it is close in spirit to the competitive model, with a tractable and unique equilibrium, and is therefore useful for empirical testing. Second, on-the-job search is an e cient response to rm heterogeneities and convex search costs. Third, the equilibrium leans towards a job ladder, where unemployed workers apply to low-productivity rms o ering low wages, and then gradually move on to more productive, higher-paying rms. With a continuum of rm types, the job ladder i strict, in the sense that there is a one-to-one correspondence between the productivity of the current employer and that of the rms she searches for. The paper also contributes methodologically, as the existence proof requires a version of Schauder's xed point theorem that is not commonly used by economists. Finally, our model o ers di erent implications for the dynamics of job-to-job transitions than existing models of random search.