Language‑model agents are deployed in finance, healthcare, law and other specialized domains. They can usually complete a task but often miss fine details, such as which filing a figure comes from in a financial report. Retraining the agent is expensive and impossible for closed‑source systems. Writing the missing know‑how into the prompt makes it long and identical for every input, while different inputs need different guidance. We propose a small advisor model that reads each input, writes structured advice, and appends it to the prompt of a frozen executor. The advisor is trained by hindsight distillation: on a graded answer pool we analyse executor failures, run several strategies, record which strategy works for each input, and let a teacher that sees grades and traces write the advice that would have helped. The advisor then learns, via supervised fine‑tuning, to produce that advice from the input alone. Because the advisor is a separate lightweight model, training cost is low and inference latency barely increases. We call this approach Hindsight Structured Advice Distillation (HSAD). On the FrontierFinance benchmark an 8B advisor raises Samaya’s proprietary research agent’s qualification rate from 52.9% to 56.6% while cutting cost by 37% compared to the agent’s high‑effort configuration. Experiments also show HSAD improves performance on WebShop, BIRD text‑to‑SQL and ExpertLongBench. Review