Wage distributions in economies with mandated minimum wage exhibit both wage dispersion and wage clustering known as the minimum wage spike. The paper builds a search-theoretic model that reconciles the two phenomena simultaneously under the assumptions of wage-posting, urn-ball matching, rm heterogeneity, and wage-dependent search cost. Numerical simulations demonstrate the potency of the model. A non-degenerate minimum wage spike and wage dispersion are obtained. The model also shows that a higher, non-binding minimum wage can be associated with greater employment (and higher wages), previously found in empirical studies.