We consider the market value of excess demand as a measure of disequilibrium. We show that, in a fixed exchange economy, there exist approximate equilibria whose measures of disequilibrium depend only on the endowments and not on the preferences. A related bound on the norm of excess demand, depending on the endowments and the approximate equilibrium price, is also obtained. We show the existence of allocations which are nearly competitive, as measured by the largest proportion of demand given up at the allocation by any trader. We use these results to obtain, for very general sequences of exchange economies, allocations giving all traders bundles close to norm to their demands. This result includes a O(1/n) rate of convergence in the case of uniformly bounded endowments.