An important problem for proving statements in multimodal categorial grammar is that even when using proof nets — which improve upon proof search in natural deduction and sequent calculus by identifying all equivalent proofs — the number of possible axiom links to consider is still enormous. We will propose several efficient strategies to reduce the number of axiom links and will evaluate the resulting combined strategy against a large number of statements in both multimodal and Lambek categorial grammars and find that we eliminate a very large number of the axiom links which do not correspond to any proof net.