How does asset encumbrance affect the fragility of intermediaries subject to rollover risk? We offer a model in which a bank issues covered bonds backed by a pool of assets that is bankruptcy remote and replenished following losses. Encumbering assets allows a bank to raise cheap secured debt and expand profitable investment, but it also concentrates risk on unsecured debt and thus exacerbates fragility and raises unsecured funding costs. Deposit insurance or wholesale funding guarantees induce excessive encumbrance and fragility. To mitigate such risk shifting, we study prudential regulatory tools, including limits on encumbrance, minimum capital requirements and surcharges for encumbrance.