This study advances signaling and screening theories by introducing the concept of "signal hierarchy," which posits that decision-makers prioritize information cues based on their perceived correlation with a firm's unobservable qualities. Moving beyond the conventional focus on single information cues, we argue that high-ranking information cues directly influence decision-making, while lower-ranking cues play a crucial secondary role by highlighting incongruencies. We apply these theoretical insights to the context of cross-border acquisitions and focus on CSR performance as an important information cue that influences the premium acquirers pay for their targets. Specifically, we use a sample of 469 cross-border acquisitions and compare the impact of CSR performance cues from rating agencies and target countries. We find that higher CSR firm ratings significantly increase acquisition premiums, while those of the target country do not. Furthermore, we find that incongruence between CSR firm ratings and target country CSR cues diminishes the baseline effect of firm CSR ratings. Our theory and findings advance our understanding of the interplay between multiple information cues, offering a new perspective on decision-making under conditions of information asymmetry.