The limits of open-ended generative models are unclear, yet increasingly important. What causes them to succeed and what causes them to fail? In this paper, we take a prompt-centric approach to analyzing and bounding the abilities of open-ended generative models. We present a generic methodology of analysis with two challenging prompt constraint types: structural and stylistic. These constraint types are categorized into a set of well-defined constraints that are analyzable by a single prompt. We then systematically create a diverse set of simple, natural, and useful prompts to robustly analyze each individual constraint. Using the GPT-3 text-davinci-002 model as a case study, we generate outputs from our collection of prompts and analyze the model’s generative failures. We also show the generalizability of our proposed method on other large models like BLOOM and OPT. Our results and our in-context mitigation strategies reveal open challenges for future research.