This paper examines ways to summarize the maturity structure of public debts using a small number of parameters. We compile a novel dataset of all promised future payments for US and UK government debt from every month since 1869, and more recently for Peru, Poland, Egypt, and Nigeria. We show that there is a unique parametric form which does not arbitrarily restrict debt issuance - portfolios of bonds with exponential coupons. Compared to the most popular alternative, this form 1) more accurately describes changes in debt maturity for these six countries and 2) gives a quite different interpretation of historical debt maturity. Our work can be applied not just to analyze past debt movements, but - because parameter estimates are relatively similar across countries - also for monitoring changes in debt maturity, including in countries where data are partial or incomplete.