A common position adopted by international lawyers on State borders is that they should be changed as little as possible, as allowing too much scope for changes to borders risks opening up a Pandora’s box of unending claims. The liberal position on international boundaries posits that the location of a State’s external boundaries matters little anyway, as the liberal State can function within any borders. The article attempts to provide a critique of these positions, and argues that another approach to borders, and particularly to boundaries at the dissolution of States, is needed. The liberal assumption does not adequately respond to boundary changes in non-liberal States. Differences between borders, and the importance attached to these differences in different contexts, have attracted little attention by international lawyers. Because the same solution often tends to lead to different results in different contexts, attempting to apply Public International Law rules, such as a modern version of uti possidetis, to boundaries in all cases of State dissolutions and new State formations, forms not only an insufficient response, but might in fact risk contravening obligations under the UN Charter to maintain international peace and security. The conflicts over the republican boundaries of the Socialist Federal Republic of Yugoslavia (SFRY) in the early 1990s exemplify that an automatic conversion of federal boundaries into international ones risks undermining long-term peaceful solutions. The final status of Kosovo, and the issue of its borders, remains a challenge for the international community. In light of the recent tensions in Kosovo existing territorial and political assumptions need to be reexamined, in order that the solution adopted for the territory accord with international obligations set out under the UN Charter.