This paper develops a model of CDS demand when investment is subject to economic fluctuations and verification is imperfect. We show that CDS overinsurance (insurance in excess of renegotiation proceeds) is procyclical and allows for greater financing of firms with positive NPV projects. In bad times, CDS overinsurance triggers the early liquidation of firms with low continuation values. Our analysis explains the optimality of CDS contracting and reconciles evidence showing that CDSs are most beneficial for firms that are safer and have higher continuation values. The model generates a number of empirical predictions and provides insights on the regulation of CDS markets.