It has historically been assumed that comparative (‘more than’, ‘fewer/less than’) and superlative (‘at most’, ‘at least’) quantifiers can be semantically analysed in accordance with their core logical–mathematical properties. However, recent theoretical and experimental work has cast doubt on the validity of this assumption. Geurts & Nouwen (2007) have claimed that superlative quantifiers possess an additional modal component in their semantics that is absent from comparative quantifiers and that this accounts for the previously neglected differences in usage and interpretation between the two types of quantifier that they identify. Their semantically modal hypothesis has received additional support from empirical investigations. In this article, we further corroborate that superlative quantifiers have additional modal interpretations. However, we propose an alternative analysis, whereby these quantifiers possess the semantics postulated by the classical model and the additional aspects of meaning arise as a consequence of psychological complexity and pragmatic implicature. We explain how this model is consistent with the existing empirical findings. Additionally, we present the findings of four novel experiments that support our model above the semantically modal account.