We study the formation of wages in a frictional search market where firms can choose either to bargain with workers or post non-negotiable wage offers. Workers can secure wage increases for themselves by engaging in on-the-job search and either moving to firms that offer higher wages or, when possible, leveraging an outside offer into a higher wage at the current firm. We characterize the optimal wage posting strategy of non-negotiating firms and how this decision is influenced by the presence of renegotiating firms. We quantitatively examine the model's unique implications for efficiency, wage dispersion, and worker welfare by estimating it using data on the wages and employment spells of low-skill workers in the United States. In the estimated steady state of the model, we find that more than 10% of job acceptance decisions made while on the job are socially sub-optimal. We also find that, relative to a benchmark case without renegotiation, the presence of even a small number of these firms increases the wage dispersion attributable to search frictions, deflates wages, and reduces worker welfare. Moving to a general equilibrium setting, we use the estimated model to study the impact of a minimum wage increase on firm bargaining strategies and worker outcomes. Our key finding is that binding minimum wages lead to an increase in the equilibrium fraction of renegotiating firms which, relative to a counterfactual in which this fraction is fixed, significantly dampens the reduction in wage dispersion and gains in worker welfare that can typically be achieved with moderate minimum wage increases. Indeed, the presence of endogenous bargaining strategies reverses the sign of the average welfare effect of a $15 minimum wage from positive to negative.