We develop an equilibrium directed search model of the labor market where workers can simultaneously apply for multiple jobs. The main result is that all equilibria exhibit wage dispersion despite the fact that workers and firms are homogeneous. Wage dispersion is driven by the simultaneity of application choice. Risk-neutral workers apply for both 'safe' and 'risky' jobs. The former yield a high probability of a job offer, but for low pay, and act as a fallback option; the latter provide with higher potential payoff, but are harder to get. Furthermore, the density of posted wages is decreasing, consistent with stylized facts. Unlike most directed search models, the equilibria are not constrained efficient.