Under market demand uncertainty, we show that quotas can result in a welfare advantage over tariffs for an importing country despite that its government does not capture any quota rents. Specifically, the conditions under which an equivalent quota yields higher expected welfare than a tariff are shown to depend on a set of economic variables. These variables include the initial tariff rate, the relative efficiency in production between home and foreign firms, the probability distribution of random demand shocks that make the quota binding or non-binding under uncertainty, as well as the variance of the stochastic market demand. The analysis of this paper has welfare implications for tariffication. (C) 2010 Elsevier Inc. All rights reserved.