Very few firms issue equity to refinance their debt in distress. This simple observation has an important effect on the predictions of capital structure models. A model in which highly-levered firms needing external finance must issue debt explains the overall underleverage puzzle, fully replicates the ‘fat’ right tail of cross-sectional leverage distribution, and produces realistic default probabilities across firms with different leverage values. The model succeeds even if bankruptcy costs are only 10% of firm’s assets, whereas the model that allows for equity issuance requires bankruptcy costs to exceed 60% in order to generate plausible average leverage.