Previous research has shown that compound word recognition involves selecting a relational meaning (e.g. “box for letters” for letterbox) out of a set of competing relational meanings for the same compound. We conducted five experiments to investigate the role of competition between relational meanings across visual and auditory compound word processing. In Experiment 1 conceptual relations judgments were collected for 604 English compound words. From this database we computed an information-theoretic measure of competition between conceptual relations – entropy of conceptual relations. Experiments 2 and 3 report that greater entropy (i.e. increased competition) among a set of conceptual relations leads to longer latencies for compounds in auditory lexical decision. Experiments 4 and 5 demonstrate the same result in two visual lexical decision studies. These findings provide evidence that relational meanings are constructed and evaluated during compound recognition, regardless of whether compounds are recognised via auditory or visual input.