Chain-of-thought (CoT) reasoning improves large language model performance on complex tasks, but often produces excessively long and inefficient reasoning traces. Existing methods shorten CoTs using length penalties or global entropy reduction, implicitly assuming that low uncertainty is desirable throughout reasoning. We show instead that reasoning efficiency is governed by the trajectory of uncertainty. CoTs with dominant downward entropy trends are substantially shorter. Motivated by this insight, we propose **E**ntropy **T**rend **R**eward (**ETR**), a trajectory-aware objective that encourages progressive uncertainty reduction while allowing limited local exploration. We integrate ETR into Group Relative Policy Optimization (GRPO) and evaluate it across multiple reasoning models and challenging benchmarks. ETR consistently achieves a superior accuracy–efficiency trade-off, improving DeepSeek-R1-Distill-7B by +9.9% accuracy while reducing CoT length by 67% across four benchmarks.

Reinforcement learning (RL) for large language models (LLMs) typically requires clear reward signals, which are often unavailable for open-ended (OE) questions where answer evaluation is ambiguous without scalable expert labeling. We investigate whether LLMs benefit from training on mixed data with varying reward clarity. Our approach combines Multiple-choice questions (MCQs), which offer clear binary rewards, with OE questions, for which we use simpler, potentially noisy rewards such as Jaccard similarity or LLM-based evaluators. We hypothesize that MCQs can stabilize training when mixed with OE questions. Our experiments show this mixed-data approach consistently improves medical question-answering performance across model scales.