Previous papers presented Witscript and Witscript 2, AI systems for improvising jokes in a conversation. Witscript generates jokes that rely on wordplay, whereas the jokes generated by Witscript 2 rely on common sense. This paper extends that earlier work by presenting Witscript 3, which generates joke candidates using three joke production mechanisms and then selects the best candidate to output. Like Witscript and Witscript 2, Witscript 3 is based on humor algorithms created by an expert comedy writer. Human evaluators judged Witscript 3's responses to input sentences to be jokes 44% of the time. This is evidence that Witscript 3 represents another step toward giving a chatbot a humanlike sense of humor.