Rejecting structural principles, like the reflexivity or transitivity of the entailment relation, provides an attractive solution to the semantic paradoxes, allowing us to give a uniform analysis and solution to the paradoxes of self-reference without having to engage in piecemeal rejection of inferential principles governing the sentential connectives. To date all of the proposed nonreflexive and nontransitive logics have been substructural companions of classical logic. In this paper we correct this by investigating the substructural companions of intuitionistic logic, and their relation to their classical counterparts.