This paper investigates whether information about fairness types can be useful in lowering dispute costs and enhancing bargaining efficiency. An experiment was conducted in which subjects were first screened using a dictator game, with the allocations chosen used to separate participants into two types. Mutually anonymous pairs of subjects then bargained, with a dispute cost structure imposed. Sorting with identification reduces dispute costs; there are also significant differences in bargaining efficiency across pairing types. Information about types is crucial for these differences and also strongly affects the relative bargaining success of the two types and the hypothetical optimal bargaining strategy.