Unlocking LLM Legal Reasoning with IRAC-Constrained Chain-of-Thought

Large language models have made remarkable progress in mathematics and code, yet legal reasoning remains substantially harder: even perfect retrieval does not yield the answer, since the model must interpret abstract rules and apply them to novel facts through multi-step argument. Prior work has approached this difficulty either by training reinforcement learning (RL) policies for retrieval-augmented reasoning or by eliciting structured reasoning from frozen models through prompting. Neither approach modifies the model's underlying reasoning policy with a domain-appropriate structure. We argue that legal reasoning in small open-source LLMs requires equipping the policy itself with such a structure, and that the IRAC framework (Issue, Rule, Application, Conclusion), standard in legal practice, is well suited to this role. We introduce IRAC-R1, a two-stage pipeline that first distills IRAC-structured reasoning traces from a stronger teacher via supervised fine-tuning, and then refines this structure with reinforcement learning under a structural reward. On Bar Exam QA, IRAC-R1 improves Qwen2.5-7B-Instruct from 47.9% to 58.1% accuracy (+10.2 points), and to 61.5% with gold-passage injection. We show that IRAC, rather than generic chain-of-thought reasoning, is responsible for the gain, and we find that retrieval, rather than reasoning, appears to be the dominant bottleneck for retrieval-augmented legal QA.