This paper highlights the role of external indebtedness and the presence of inflationary inertia in order to assess the effectiveness and sustainability of inflation targeting during disinflation episodes. As the recent Argentinian experience illustrates, a sluggish inflation rate and a significant currentaccount deficit may make the stabilization process difficult. To illustrate the point, we build a model that shows that, when inflation adjusts fast, the target may be achieved without building too much external debt. But if inflation adjusts slowly, an excessive build-up of external debt could lead to an increase in the risk premium, a sudden shortage of foreign exchange, and the eventual collapse of the inflation-targeting regime.