Star Trek: The Next Generation/Recap/S3/E02 The Ensigns of Command

The Enterprise receives a message from the Sheliak, insisting they remove all humans from a planet that the Sheliak have the legal right to colonize. The Federation has no record of a colony there - there's radiation that would normally be lethal to humans - but it turns out that, about a century ago, a colony ship went off course and ended up there. They build a radiation shield, settled in, and by now have grown to a population of 15,000 or so.

The evacuation will take weeks by shuttlecraft (the radiation also messes up the transporters), but the Sheliak are arriving in four days; Picard negotiates with the Sheliak, who keep insisting on not giving them any extra time. Meanwhile, the colonists don't want to evacuate at all (screw the treaties, many of their ancestors died getting that shield built!), and Data must convince them otherwise.


 * Bothering By the Book: The Sheliak constantly stand on the exact wording of their very long peace treaty with the Federation...
 * Loophole Abuse: ...until Picard reads through it himself, then exploits a loophole that would delay their plans by six months. He then hangs up on them and strolls about the bridge for a minute when they call back.
 * Curb Stomp Battle: Data finally overcomes the colonists' pride by demonstrating that one android with a hand phaser can seriously wreck their equipment, then stating that the Sheliak are packing much bigger weapons and will blow them away from orbit without a second thought.