In this paper, we define deficit sustainability by requiring formally that both the discounted debt vanish asymptotically and the undiscounted debt be bounded. Thus, a new necessary condition and a new testing procedure emerge. We propose a new test statistic and prove that its limiting distribution is standard normal, N(0, 1). Its finite- sample distribution differs from N(0, 1), however, mainly because it has fat tails, so we derive empirical critical values using simulations. Using the new test and United States (US) quarterly data, the conclusions of three earlier papers that fail to reject the sustainability of the US budget or current-account deficit are reversed.