Limerick generation exemplifies some of the most difficult challenges faced in poetry generation, as the poems must tell a story in only five lines, with constraints on rhyme, stress, and meter. To address these challenges, we introduce LimGen , a novel and fully automated system for limerick generation that outperforms state-of-the-art neural network-based poetry models, as well as prior rule-based poetry models. LimGen consists of three important pieces: the Adaptive Multi-Templated Constraint algorithm that constrains our search to the space of realistic poems, the Multi-Templated Beam Search algorithm which searches efficiently through the space, and the probabilistic Storyline algorithm that provides coherent storylines related to a user-provided prompt word. The resulting limericks satisfy poetic constraints and have thematically coherent storylines, which are sometimes even funny (when we are lucky).