We propose a theory of leverage dynamics based on a parsimonious model with a cashflow process subject to diffusion and jump shocks, external financing through short-term debt and equity, and crucially equity issuance costs. We show that both plausible average leverage outcomes and observed leverage dynamics can be explained by firms’ efforts to avoid incurring equity issuance costs. Paradoxically, it is the high cost of equity issuance that causes the firm to keep leverage low, in contrast to the predictions of Modigliani-Miller and Leland tradeoff and Myers’ pecking-order theories. The marginal source of external financing on an on-going basis is debt. Leverage can only increase as a result of losses. When the firm is at its target leverage any additional profit is paid out, and when leverage reaches the firm’s endogenous debt capacity any additional loss either triggers a costly recapitalization or a default. When leverage is close to the firm’s target, it tends to revert to target, but beyond a certain point the expected change in leverage is positive and the firm enters a leverage death spiral.