Test-time compute methods can significantly improve the reasoning capabilities and problem-solving accuracy of large language models (LLMs). However, these approaches require substantially more computational resources, with most compute wasted on exploring low-diversity branches where the model already exhibits high confidence. We observe that a small subset of uncertain reasoning steps has a disproportionately large impact on final prediction accuracy, and branching at these critical junctures tends to yield more diverse and higher-quality candidate reasoning steps. We propose Entropy-Gated Branching (EGB), which branches only at high-uncertainty steps and prunes expansions with a lightweight verifier. On mathematical and financial reasoning benchmarks, EGB improves accuracy by 22.6% over standard inference while operating 31%-75% faster across math benchmarks than test-time beam search with higher performance. Our results show that dynamic resource allocation during inference can substantially improve both efficiency and effectiveness, offering a more scalable pathway to enhanced LLM reasoning capabilities.