It sometimes happens that when someone asks a question, the addressee does not give an adequate answer, for instance by leaving out part of the required information. The person who posed the question may wonder why the information was omitted, and engage in extensive processing to find out what the partial answer actually means. The present study looks at the neural correlates of the pragmatic processes invoked by partial answers to questions. Two experiments are presented in which participants read mini-dialogues while their Event-Related brain Potentials (ERPs) are being measured. In both experiments, violating the dependency between questions and answers was found to lead to an increase in the amplitude of the P600 component. We interpret these P600-effects as reflecting the increased effort in creating a coherent representation of what is communicated. This effortful processing might include the computation of what the dialogue participant meant to communicate by withholding information. Our study is one of few investigating language processing in conversation, be it that our participants were 'eavesdroppers' instead of real interactants. Our results contribute to the as of yet small range of pragmatic phenomena that modulate the processes underlying the P600 component, and suggest that people immediately attempt to regain cohesion if a question-answer dependency is violated in an ongoing conversation.