Law enforcement authorities (LEAs) increasingly need to obtain digital evidence that is stored or controlled across borders. As a result, States increasingly exercise enforcement jurisdiction extraterritorially by imposing investigative measures on service providers that possess or control data outside the territory, without the State’s LEAs physically entering another State’s territory. This exercise of ‘investigative jurisdiction’ seemingly conflicts with the longstanding prohibition of the exercise of extraterritorial enforcement jurisdiction in international law. This article argues that given the development of State practice, longstanding jurisdictional principles should adapt to global technologies. Consistent with the principle of comity, this article conceptualises a limited form of investigative jurisdiction that respects sovereignty and minimises conflicts of law.