A plethora of jailbreaking attacks have been proposed to obtain harmful responses from safety-tuned LLMs. In their original settings, these methods all largely succeed in coercing the target output, but their attacks vary substantially in fluency and computational effort. In this work, we propose a unified threat model for the principled comparison of these methods. Our threat model combines constraints in perplexity, measuring how far a jailbreak deviates from natural text, and computational budget, in total FLOPs. For the former, we build an N-gram model on 1T tokens, which, in contrast to model-based perplexity, allows for an LLM-agnostic and inherently interpretable evaluation. We adapt popular attacks to this new, realistic threat model, with which we, for the first time, benchmark these attacks on equal footing. After a rigorous comparison, we not only find attack success rates against safety-tuned modern models to be lower than previously presented but also find that attacks based on discrete optimization significantly outperform recent LLM-based attacks. Being inherently interpretable, our threat model allows for a comprehensive analysis and comparison of jailbreak attacks. We find that effective attacks exploit and abuse infrequent N-grams, either selecting N-grams absent from real-world text or rare ones, e.g. specific to code datasets.