A truthmaker for a proposition P is exact if it contains nothing irrelevant to P. What are the exact truthmakers for necessitated propositions? This paper makes progress on this issue by showing how to extend Fine’s truthmaker semantics for intuitionistic logic to an exact truthmaker semantics for intuitionistic modal logic. The project is of interest also to the classical logician: while all distinctively classical theorems may be true, they differ from the intuitionistic ones in how they are made true. This (...) sheds new light on the status of the T and B axioms. (shrink)