A basic theme of microeconomics is the equivalence of price and quantity controls under certainty. The welfare comparison of these two control modes under uncertainty has been undertaken recently in two different contexts. Weitzman (1974) initiated the comparison of these two modes in the context of a planning authority which faces uncertainty about the costs and benefits of producing a particular good. It chooses between controlling quantities and setting a price for producers. His analysis has been developed by Laffont (1977), Ireland (1977), Malcomson (1978), Weitzman (1978) and Yohe (1978). A second area of analysis, to which this paper contributes, is the welfare comparison of the two control modes in the context of international trade under uncertainty. In this context, prices are determined by market choices by both sellers and buyers but the government intervenes in the market, e.g. through a quota or a tariff. Fishelson and Flatters (1975) and Young (1979a) have compared the use of quotas and ad valorem tariffs by a large country to improve its terms of trade. For a small country, Dasgupta and Stiglitz (1977) and Young (1980) have compared the two instruments when they are constrained to raise a fixed expected tariff revenue; Pelcovits (1976) has compared the two instruments when they are constrained to yield a fixed level of expected imports. Anderson (1978) has shown that, for a small country, a specific tariff yields higher domestic expected consumer's surplus than the mean-equivalent import quota. For a large country, he showed that a specific tariff yields higher world expected consumer's surplus than the mean-equivalent quota. It is natural to compare the welfare effects of quotas, ad valorem tariffs and specific tariffs under uncertainty because there are the most widely used and easily administered instruments for restricting trade. However, none of the above authors have considered what policy would be optimal for the objective that they consider. This paper shows that the answer to this question can be surprisingly simple and general. Our results should be compared to Weitzman's recent results (1978) on the optimal form of controls for a planning authority.