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When an AI agent calls an API and hits a validation error, it needs more than what went wrong -- it needs what to do next. A self-reflective API returns, on validation failure, a machine-readable recovery\this http URL[] payload sufficient for the agent to repair the request and retry without external reasoning. On a leak-audited pilot ($N{=}30$ per cell, 3 LLMs, 10 adversarial tasks), structured suggestions lift task-completion rate by $+36.7$--$40.0$pp over plain-English diagnoses on Anthropic models (Fisher's exact $p \le 0.0022$), at $1.8$--$2.2\times$ better per-success token efficiency. The lift is not significant on gpt-4o-mini ($p{=}0.435$); a second-domain replication on a billing API confirms the pattern. The comparison only holds after auditing two undocumented classes of answer leakage in LLM benchmarks. We shipaudit\_prompt\this http URL as reusable CI infrastructure. Code and data: this https URL.