Reasoning Large Language Models can improve problem-solving performance through deliberative inference, but invoking slow reasoning for every input is computationally expensive and often unnecessary. We propose IDPR, a framework for response-conditioned inhibitory deliberation. IDPR first generates a concise intuitive answer and then uses an inhibition controller to decide whether that specific response should be released or suppressed in favor of slow reasoning. Unlike input-only routers, the inhibition controller conditions on the fast answer and fast-side evidence, including confidence, logit margin, parseability, and generation cost. We train the controller from paired fast-slow outcomes and select the inhibition threshold on a held-out validation set under an accuracy-first slow-call budget. On a held-out 5,000-example mathematical reasoning test set, IDPR invokes slow reasoning on only 8.20% of examples and improves accuracy from 47.90% to 48.92%. Under the same slow-call budget, random routing decreases accuracy to 46.76%, while the strongest confidence-based baseline reaches 48.22%. IDPR also achieves the highest corrective precision, showing that response-conditioned inhibition better identifies fast answers that benefit from slow reasoning.