Descriptions of a dynamic warning system usually assign the system certain diagnostic values. Operators should adjust their responses to these values when considering the output of the system for their decisions. This approach is not necessarily appropriate for complex systems that are controlled by human operators. Here the operators' actions are likely to change the frequency of events that should trigger a warning. Consequently the operator will change the predictive value of a warning system that is imperfectly correlated with the monitored events. In general its diagnostic value decreases for better operators. This phenomenon is demonstrated on the example of binary warnings about binary events, and an empirical demonstration of the phenomenon is provided in an experimental study of a process control task. Actual or potential applications of this research include improved understanding of the determinants of operators' responses to warnings, which should help in the design of better warning systems.