Two Hilbert calculi in the use-restricted relevance tradition of Anderson and Belnap are presented. One yields Anderson and Belnap’s conjunctive version of the so-called “entailment theorem,” whereas the other yields the implication-iterated version. In contrast to previous such use-restricted calculi, those presented in this paper apply to arbitrary strengthenings of the weak contractionless logic B without need for modifying the use-conditions. As such they help to identify the core idea of the “use-account” of relevance.