Previous research has suggested that the conceptual representation of a compound is based on a relational structure linking the compound’s constituents. Existing accounts of the visual recognition of modifier–head or noun–noun compounds posit that the process involves the selection of a relational structure out of a set of competing relational structures associated with the same compound. In this article, we employ the information-theoretic metric of entropy to gauge relational competition and investigate its effect on the visual identification of established English compounds. The data from two lexical decision megastudies indicates that greater entropy (i.e., increased competition) in a set of conceptual relations associated with a compound is associated with longer lexical decision latencies. This finding indicates that there exists competition between potential meanings associated with the same complex word form. We provide empirical support for conceptual composition during compound word processing in a model that incorporates the effect of the integration of co-activated and competing relational information.