We consider an asymmetric duopoly producing a homogeneous commodity and facing a competitive demand. Our model incorporates two asymmetries. The first one is relative to the performance indices. Indeed, we assume that one of the player maximizes its profit and the second one, being eager to earn hard currencies, maximizes its revenue. The second asymmetry involves a security (or diversification) constraint which states that the second player is not allowed to sell more than a certain proportion of the quantity sold by its rival. This game is an abstraction of the European natural gas market during the eighties. Cournot and Stackelberg equilibria are characterized and compared. An assessment of the impact on consumers and producers of the security constraint is also made.