Large language models achieve remarkable performance via extended chain-of-thought (CoT) reasoning, yet this lengthy process incurs substantial inference overhead. Existing CoT compression methods struggle with inflexible manual length budgets, computationally expensive multi-stage training pipelines, and fragile scalability restricted to small models. We propose **HMPO** (**H**ybrid **M**edian-length **P**olicy **O**ptimization), a cost-effective, single-stage reinforcement learning framework. HMPO efficiently compresses CoT via three synergistic components: an *adaptive median-based budget* derived from successful rollouts to eliminate manual tuning, a *cosine-decay token reward* for smooth length penalization, and a *multiplicative reward formulation* that substantially mitigates trivial reward hacking by strictly prioritizing answer correctness. Trained exclusively on mathematical data, HMPO generalizes seamlessly across math, code, science, and instruction-following tasks. Extensive experiments scaling from 9B to 122B parameters across dense and Mixture-of-Experts (MoE) architectures demonstrate that HMPO achieves **19%–46% token compression with negligible accuracy degradation**, all while drastically reducing training costs compared to existing multi-stage baselines.