I consider the problem of assigning agents to objects where each agent must pay the price of the object he gets and prices must sum to a given number. The objective is to select an assignment-price pair that is envy-free with respect to the true preferences. I prove that the proposed mechanism will implement both in Nash and strong Nash the set of envy-free allocations. The distinguishing feature of the mechanism is that it treats the announced preferences as the true ones and selects an envy-free allocation with respect to the announced preferences.This research was undertaken with support from the European Community's Phare ACE Programme 1998 (contract number P98-2007-S). The content of the publication is the sole responsibility of the author and it in no way represents the views of the Commission or its services. Financial support from the Spanish Ministry of Science and Technology through grant BEC2002-02130 is gratefully acknowledged.