In 2071, roughly fifty years after an accident with a hyperspace gateway made the Earth almost uninhabitable, humanity has colonized most of the rocky planets and moons of the Solar System. Amid a rising crime rate, the Inter Solar System Police (ISSP) set up a legalized contract system, in which registered bounty hunters, also referred to as "Cowboys", chase criminals and bring them in alive in return for a reward.

The Quick Draw McGraw Show is the third cartoon television production created by Hanna-Barbera, starring an anthropomorphic cartoon horse named Quick Draw McGraw. The series featured 3 cartoons per episode, one each by Quick Draw McGraw & Baba Looey, father and son dog duo Augie Doggie & Doggie Daddy, and cat and mouse detectives Snooper & Blabber.