Division of a resource among multiple agents is a frequent problem in multiagent systems and fair, efficient, and decentralized allocation procedures are highly valued. A division of a resource or good is envy-free when every agent believes that its share is not less than anyone else’s share by its own estimate. As envy-free procedures are not efficient (in the sense of Pareto optimality) we have previously worked on improving the efficiency of such envy-free division procedures among two agents using models of other agents’ utility functions. In this paper, we extend that work by devising an anytime algorithm that increases the efficiency of the envy-free allocation. The procedure also has the desired property of envy-freeness.