Latin American economies are exposed to substantial external vulnerability. Domestic imbalances and terms of trade shocks are often exacerbated by sharp shifts in the net supply of external capital (sudden stops). At times, these sudden stops can be the main shock. In this paper we explore ways of overcoming external vulnerability, drawing lessons from a detailed comparison of the response of Chile and Australia to recent external shocks and from Australia's historical experience. We argue that in order to understand sudden stops and the mechanisms to smooth them it is useful to identify and then distinguish between two inter-related dimensions of investors' confidence: country-trust and currency-trust. Lack of country-trust is the fundamental problem behind sudden stops. Lack of currency-trust in turn weakens a country's ability to deal with sudden stops and real external shocks. We discuss steps aimed to improve these two dimensions of investors' confidence in the medium run, and policies to reduce the impact of country-trust and currency-trust weaknesses in the short run.