What makes an inference robust? Sentences like '*First year students are allowed/required to take logic or semantics*,' with disjunction in the scope of an existential or universal modal strongly suggest that first year students are allowed to take logic and allowed to take semantics. This inference is generally referred to as ‘free choice’ in the case of existential modals, and ‘distributive’ in the case of universal ones. A prominent approach treats both of these inferences as scalar Implicatures (SIs). Experimental results, however, show that these inferences are more robust, faster to process, and easier to acquire than regular SIs. One response posits that this behavior stems from the alternatives that derive them. We present a series of experiments that test this hypothesis, comparing positive disjunctive sentences to variants with negation and conjunction, for which the SI approach predicts similar inferences for similar alternatives. We show that while these inferences are indeed robust for disjunction, the same is not true for these variants. These findings are challenging for the hypothesis that the type of alternatives involved is responsible for differences in robustness. And more generally are challenging for any unified account of these inferences, whether based on implicature or not. We outline a hybrid account treating the more robust inferences as entailments and the less robust ones as implicatures and we argue that comparing inferences in terms of robustness is an important perspective to learn more about the nature of those inferences and the relation between them.