This article outlines the US Supreme Court's approach to the habeas corpus entitlements of suspected terrorists detained in Guantánamo Bay and argues for the extension of constitutional habeas corpus rights to them. The article considers two ways in which the Supreme Court might carry out this task: first, ‘the territorial approach’ (based on domestic legal principles of ‘unincorporated territories’ and principles of leasehold), and secondly, ‘the extraterritorial approach’ (based on international purposive approaches to the reach of human rights treaties exemplified by the European Court of Human Rights' Article 1 jurisprudence). For reasons of effectiveness of protection, the Article expresses a clear preference for the latter. The House of Lords decision in R (Al-Skeini) v Secretary of State for Defence (2007) is proposed as a template for such a development. Finally the article refutes arguments rejecting such a development based on the ‘trade-off thesis’ and perceptions of judicial competence.