We study the financing of speculative asset-market booms in a standard framework with heterogeneous beliefs and short-sales constraints. Cash-constrained optimists use their asset holdings as collateral to raise debt financing from less optimistic creditors. Through state-contingent refinancing, short-term debt allows the optimists to reduce debt payment in upper states which they assign higher probabilities to, but at the expense of greater rollover risk if the asset fundamental deteriorates at the debt maturity. In contrast, long-term debt allows the optimists to hedge their financing cost in downturns. Our model identifies distinctive effects of initial and future belief dispersion in driving a short-term credit boom, and shows that the optimists' debt-maturity and leverage choices can directly affect the asset market equilibrium.