Two-step immigration is now a well-established policy strategy in countries such as Australia, Canada, and the U.S. to retain so-called 'highly skilled,' or higher-wage, immigrants. However, as this paper argues, the specific recruitment and retention of post-secondary international students in some contexts has become a distinct three-step form of immigration, shifting the role of higher education in society. The term "edugration"--an amalgamation of 'education' and 'immigration'--is proposed to describe this system. This paper also contends that "edugration" presents an ethically wicked problem (Rittel & Webber, 1973), requiring not only increased attention from higher education, international education, and (im)migration scholars, but also a shift in our analytic approach. [The publication year (2022) on the .pdf is incorrect. The correct year is 2021.]