How should the government choose the maturity structure of its debt? In the presence of uncertainty and distortionary taxation, debt policy can improve welfare by smoothing taxes across states and over time. When investors are risk averse, equilibrium expected rates of return are generally higher on debt instruments with good tax smoothing properties since investors demand a risk premium on securities that have low payoffs in bad states of the world. A benevolent government therefore needs to trade off the benefits of tax smoothing against the associated increase in average interest costs when choosing its optimal debt portfolio. The paper provides numerical examples of optimal policies in a three-period incomplete markets model where the government makes use of two debt instruments, long-term and short-term noncontingent nominal bonds. The basic prescription is to borrow long and invest short, in spite of the fact that equilibrium average interest costs are higher on long-term debt than on short-term debt. The resulting welfare gains are close to what the government could achieve with a complete set of state contingent securities. If the government is prohibited from investing, it can still significantly improve outcomes by borrowing long-term rather than short-term.