What makes an asset a “safe asset”? We study a model where two countries each issue sovereign bonds to satisfy investors' safe asset demands. The countries differ in the float of their bonds and their resources/fundamentals available to rollover debts. A sovereign's debt is more likely to be safe if its fundamentals are strong relative to other possible safe assets, but not necessarily strong on an absolute basis. Debt float can enhance or detract from safety: If global demand for safe assets is high, a large float can enhance safety. The large float offers greater liquidity which increases demand for the large debt and thus reduces rollover risk. If demand for safe assets is low, then large debt size is a negative as rollover risk looms large. When global demand is high, countries may make fiscal/debt-structuring decisions to enhance their safe asset status. These actions have a tournament feature, and are self-defeating: countries may over-expand debt size to win the tournament. Coordination can generate benefits. The model sheds light on the effects of “Eurobonds” – i.e. a coordinated Euro-area-wide safe bond design. Eurobonds deliver welfare benefits only when they make up a sufficiently large fraction of countries' debts. Small steps towards Eurobonds may hurt countries and not deliver welfare benefits.