This is set in Asimov's Trantor-centered Galactic Empire universe.
Story summary.This is the story of Loodun Antyok, a veteran bureaucrat of Empire & Empire's "Civilian Supervisor" for Cepheid affairs on a world called Cepheus 18. Cepheids are intelligent aliens that have recently been made subjects of Empire & who don't like the idea of being human subjects a bit.
Wily Antyok will game the officialdom as well as some people with their own agenda regarding Cepheus, including Tomor Zammo who wants to dissect them in lab as animals, to ensure they migrate to one of the Magellanic Clouds - so they will have a galaxy of their own to conquer.
Title refers to the position of aliens in human dominated galaxy. They've run across a blind alley as far as colonizing of the galaxy is concerned, since humans already own it.
Fact sheet.First published: Astounding, March 1945.
Listed among the stories from John Campbell's Astounding/Analog.
Related: Asimov's works; bureaucracy in fiction.