Humorous stimuli, like jokes and cartoons, are assumed to contain a central incongruity in a specific constellation of opposition and overlap that is essential to their humorousness. Many stimuli also contain additional incongruities that the audience usually overlooks, but that may be needed to create the setup for the main incongruity, e.g., animals that talk, space aliens, an Italian, an American, and a Russian sharing a language. Two of the studies described in the present paper investigated the effect of such backgrounded incongruities by removing them from a set of jokes and cartoons and testing how this affects humor processing and appreciation. A third study investigated whether the elimination of a backgrounded incongruity influences the position of a humorous stimulus on the incongruity-resolution and nonsense humor continuum. Methods included computer-based stimulus rating and self-explanations by the participants. The results suggested that backgrounded incongruities influence humor appreciation because their elimination leads to lower funniness and higher aversion. Furthermore, the backgrounded incongruities contribute strongly to the perceived absurdity of a joke. When they are removed, the jokes are perceived less to be nonsense humor but more as incongruity-resolution humor.