Here we present a model of a subtype of one-line jokes (not puns) that describes the relationship between the connector (part of the setup) and the disjunctor (often called the punchline). This relationship is at the heart of what makes this common type of joke humorous. We have implemented this model in a system, DisS (Disjunctor Selector), which, given a joke set-up, can select the best disjunctor from a list of alternatives. DisS agrees with human judges on the best disjunctor for one typical joke, and we are currently testing it on other jokes of the same sub-type.