Sentences involving embedded disjunctions give rise to distributive and free choice inferences. These inferences exhibit certain characteristics of Scalar Implicatures (SIs) and some researchers have proposed to treat them as such. This proposal, however, faces an important challenge: experimental results have shown that the two inferences are more robust, faster to process, and easier to acquire than regular SIs. A common response to this challenge has been to hypothesise that such discrepancies among different types of SIs stems from the type of alternatives used to derive them. That is, in contrast to regular SIs, distributive and free choice inferences are computed on the basis of sub-constituent alternatives, which are alternatives that are formed without lexical substitutions. This paper reports on a series of experiments that tested this hypothesis by comparing positive, disjunctive sentences giving rise to the two inference types to variants of these sentences involving either negation and conjunction, or negation and disjunction, for which the implicature approach predicts similar inferences on the basis of the same type of alternatives. The investigation also included deontic and epistemic modality, different positions of negation, and was extended to similar comparisons with simple disjunctions and the related ignorance inferences they give rise to. Our results show that, while the inferences are indeed quite robust in the disjunctive cases, regardless of whether negation is present or not, the inferences that their negative, conjunctive variants give rise to are not. These findings are challenging for the hypothesis that the type of alternatives involved in SI computation is a major factor responsible for differences in robustness. We outline two possible alternative explanations of our data.