We propose a new tractable general framework for sorting – composite sorting. Composite sorting comprises of (1) distinct workers being assigned to the same job and (2) a given worker type simultaneously being part of both positive and negative sorting. We show that composite sorting generically arises in a class of sorting models when fixed investments can mitigate the variable costs of mismatch. We develop a complete characterization of equilibrium sorting as well as the corresponding equilibrium wages. Wages exhibit a local hierarchical structure meaning the relative wages depend solely on sorting patterns within narrow skill groups. Using this framework, we study within–job wage dispersion and demonstrate that quantitatively composite sorting may explain a sizable portion of wage dispersion within occupations in the United States.