Research on organizational signalling tends to focus on the effects of isolated or congruent signals, assuming highly rational responses to those signals. In this study, we theorize about the cognitive processes associated with the attention paid to and interpretation of multiple, often incongruent signals that organizations send to consumers, financiers, and other stakeholders who make organizational assessments. Contributing a cognitive perspective of signal attention and interpretation, alongside the introduction of signal sets, we provide a more complete picture of how organizational signalling unfolds in the field. Our research opens new frontiers for future inquiry into the cognitive foundations of signal attention, multi‐signal interpretation, and incongruent signals.