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Although Mortimer started the fight, Mickey and Mortimer became more like equal adversaries soon into the short. The short then became a "Spy vs. Spy"-type short where one character kept trying to wreck the other more and more. The short maintained that format right up to the end, where what first seemed like a moral of the story wound up satirized. It was very original to cast Mickey in this format as the format allowed him to sometimes get really nasty. Watch for the chainsaw scene, and note who ultimately destroyed both homes, and how.
The short was also highlighted by the cartoon physics methods Mickey and Mortimer used to set up their decorations. I especially liked Mickey's instant grow Christmas tree, and the switches that moved their houses around like they were parts in a machine. The short also had some well placed cameos among the decorations.
By the way, this short is called "Mickey's Christmas Crisis," not "Mickey's Christmas Chaos." (Webmaster's note: I know the short was called "Chaos" when it was originally shown on "MouseWorks." Is it possible the title was changed for the showing on "House of Mouse?")