Story about tricking the earth empire into saving hopeless aliens

I'm hoping to identify an SF story (read it at least 20 years ago, I think), where Earth has set up a base on a distant world, and when the locals see how advanced they are, they quietly give up on themselves, and stop having children.

The governor (or similar) from earth has conversations with the earth military commander, talking about how they really wish they could get earth to leave the natives to themselves, but it won't happen. The military commander thinks the system is broken, but the governor suggests the there are ways to "make the system work for you".

Some time later the governor privately suggests to the commander that maybe teaching the locals about ships and piloting might encourage them to take new interest in life, and the commander requests permission for this from the military.

At some meeting, the governor somehow gets the locals (the locals may be slightly telepathic?) to express interest in some very fragile art form he has one of, which prompts someone to request shipment of many of them as gifts for the natives.

Because they're so fragile, this gets a lot of huge transports ships to the planet, and since meanwhile the natives have learned how to fly, they steal them and emigrate en masse, vanishing into the void.

The military guy accuses the governor of setting this all up (to the reader this is clearly true), but there's no proof, and the story closes with the governor reminding the commander of what he had said about making the system work for you.

What is the name of this story?

Answer

Blind Alley by Isaac Asimov. It's printed in The Complete Stories, Volume 2 amongst other places.

The few remaining members of the only intelligent non-human alien race the Galactic Empire has discovered have been removed from their dying planet and transferred to the much more pleasant Cepheus-18 (hence their name, "Cepheids"). The planet is a combination of zoo, laboratory, and reservation for the creatures. The scientists that study the Cepheids differ on whether to treat them as sentient beings or as animals, but agree that the aliens are in danger of extinction as they have ceased to reproduce. While the administrator already suspects that this is due to a certain ennui, the Cepheids' leader later admits personally that while their race would likely have soon died out on its dangerous home world as their science only covered their biological needs; they have nothing to live for in a galaxy completely ruled by humans who provide for all their physical needs, and they are prohibited from leaving the Empire.

The civilian supervisor, a career administrator, attempts to help the creatures using his thorough knowledge of the Imperial bureaucracy. By carefully orchestrating a leak of a report that he encouraged a subordinate to make, he causes the bureaucracy to make the reproduction problem a priority. Then, he arranges for the Cepheids to receive pilot training under the guise of providing them with a challenge, and finally by using a crude form of telepathy during an interview with their leader, he hints to the leader to express interest in a bulky object so that he can manipulate the bureaucracy into arranging for a fleet of hundreds of spaceships to deliver a large quantity of these to the Cepheids. His plan works; the Cepheids commandeer the ships leaving the humans off guard without any nearby ships with which to mount a pursuit, and it is hinted that they have left for the Magellanic Clouds to find a new world of their own. The supervisor has protected himself from any blame for the escape by his ingenious bureaucratic maneuvers, and is placed on leave pending reassignment.

_{Plot summary from Wikipedia}