Grannan and Swindle considered a model in which molecules of several types of reactant land on a catalytic surface. When two different reactants find themselves adjacent, they diffuse from the surface and leave the sites vacant. They showed that if tile rate of bonding onto the surface of one reactant is sufficiently close to one, then the surface becomes poisoned by that type. In this paper we show that a sufficient condition for poisoning is that one reactant should bond at rate greater than that of the other reactants combined.