Governments frequently allocate resources at low prices and on a first-come-first-served basis because of reasons of equity and a concern for the poor. However, bureaucrats who distribute these resources often take bribes. This paper develops a rigorous model to analyze the distributional, efficiency and public policy implications of bribery in such situations. It is shown that at low prices, the poor would choose to wait while the rich would pay the bribe to obtain the rationed commodity. If the good is in extreme short-supply, the bureaucrat would allocate all units to the rich and the poor would be excluded. Contrary to the assertion made in the corruption literature, bribery may not enhance allocative efficiency.