A major drawback of reasoning models is their excessive token usage, inflating computational cost, resource demand, and latency. We show this verbosity stems not from deeper reasoning but from reinforcement learning loss minimization when models produce incorrect answers. With unsolvable problems dominating training, this effect compounds into a systematic tendency toward longer outputs. Through theoretical analysis of PPO and GRPO, we prove that incorrect answers inherently drive policies toward verbosity \textit{even when} $γ=1$, reframing response lengthening as an optimization artifact. We further uncover a consistent correlation between conciseness and correctness across reasoning and non-reasoning models. Building on these insights, we propose a two-phase RL procedure where a brief secondary stage, trained on a small set of solvable problems, significantly reduces response length while preserving or improving accuracy. Finally, we show that while GRPO shares properties with PPO, it exhibits collapse modes, limiting its reliability for concise reasoning. Our claims are supported by extensive experiments.

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