The High Court has long struggled with the constitutional status of military tribunals established to hear disciplinary charges against service personnel. The Court's judgments reveal three distinct theories on this issue. The first view holds that military tribunals exercise judicial power, but not 'the judicial power of the Commonwealth' within the meaning of s 71 of the Constitution. The second view holds that the power in question is not judicial power at all for constitutional purposes. The third view holds that the power is 'the judicial power of the Commonwealth', but can be exercised by courts martial under a limited exception to the rules set out in Chapter III of the Constitution. The first view dominated the High Court's reasoning until Lane v Morrison (2009) 239 CLR 230, where the judges endorsed the second view. This article contends that the first and second views pose insuperable difficulties when placed in their broader constitutional context. The authors therefore argue for the third interpretation. They further argue that the constitutional basis for the third view strongly implies that military tribunals may only exercise jurisdiction over offences by military personnel that relate to service discipline.