We assess the sustainability of the public finances of Greece, Ireland, Italy, Portugal and Spain (GIIPS), allowing for possible non-linearities in the form of threshold behaviour of the fiscal authorities. We provide some evidence of fiscal sustainability when debt gets too high relative to a threshold which is not necessarily fixed but varies with the level of debt relative to its recent history and/or the occurrence of a financial crisis. However, the Greek and Italian debt-to-GDP threshold levels (over which adjustment takes place) exceed 87% and rise further in periods of financial crises. This arguably adds to international investors' concerns, and as a result, raises the yields demanded for holding Greek and Italian debt. As debt is rolled over at high interest rates, fiscal prospects worsen making default more likely and adding to contagion effects from one Eurozone country to another.