Long chain-of-thought~(CoT) reasoning improves the problem-solving capability of large reasoning models~(LRMs), but often incurs substantial inference cost and overthinking. Existing efficiency methods primarily rely on prompting, post-hoc compression, or length-regularized optimization; these approaches can be sensitive to model scale, depend on external estimators, or under-allocate reasoning to difficult instances. We propose \textbf{Draft-Thinking}, a lightweight adaptation framework that learns a \textit{model-adapted draft CoT}: a compact, self-contained working derivation that directly supports the final answer. We identify a \textbf{Cross-Scale Draft Mismatch}: concise traces generated by a strong teacher can be too sparse for a smaller target model. To address this mismatch, \textbf{Progressive Draft Adaptation} first transfers a concise reasoning-form prior through supervised fine-tuning (SFT) and then applies two-stage reinforcement learning (RL) with progressively harder data and relaxed response budgets to calibrate the reasoning granularity to the target model. The method requires neither post-hoc trajectory compression nor an explicit length-penalty reward. At inference time, draft, adaptive, and step-by-step prompts provide efficiency-oriented, balanced, and detailed reasoning modes, respectively. The step-by-step mode largely preserves the original model's accuracy while using fewer tokens. With only 847 training problems and 120 RL optimization steps, Draft-Thinking substantially reduces reasoning cost across six mathematical and scientific reasoning benchmarks. On MATH500, its draft mode reduces the average response length from 5,668 to 986 tokens, an 82.6\% reduction, while achieving 90.6\% accuracy compared with 93.0\% for the original long CoT model.

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