"Two Dozen and One Greyhounds" was written by Mike Scully. Bob Anderson is the director of the episode. Al Jean and Mike Reiss came up with the story of the episode. They got the idea after seeing the movie "One Hundred and One Dalmatians". David Mirkin said as a joke that they like to take ideas from Disney. For example, another episode called "Simpsoncalifragilisticexpiala(Annoyed Grunt)cious" is a parody of the movie "Mary Poppins". Mirkin thought it was great that they could use ideas from Disney in a "completely legal way".