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Description: Scalar inferences (SIs) may introduce either an upper-bound or a lower-bound on the dimension over which the scalar word quantifies. We conducted two experiments to test whether the cognitive load effects previously reported for upper-bounding SIs generalise to lower-bounding SIs. Using the dual-task methodology, we compared the availability of upper-bounding SIs arising from positive sentences (e.g., Some As are Bs) with that of lower-bounding SIs arising from their negative variants (e.g., Some As are not Bs, Not all As are Bs) under various cognitive loads. Using three scalar expressions, we obtained results which show that lower-bounding SIs involve comparable cognitive demands as their upper-bounding counterparts. These findings challenge a recent hypothesis explaining cognitive load effects in reference to SI polarity and suggest instead that these effects are relatively consistent across different types of SIs.