Large language models (LLMs) excel at complex reasoning tasks but often suffer from overconfidence and computational inefficiency due to fixed computation budgets and miscalibrated confidence estimates. We present a novel framework for computationally efficient, trustworthy reasoning under uncertainty, introducing two complementary techniques: Diversity-Aware Self-Signal Dilution (DASD) and Convergent Adaptive Weighted Sampling (CAWS). DASD operates in an unsupervised manner to dilute overconfident, semantically redundant reasoning paths, thereby producing better-calibrated internal confidence estimates. CAWS dynamically allocates computational resources at inference time by aggregating these signals and terminating computation once answer dominance and stability are achieved. Comprehensive experiments across three reasoning datasets demonstrate that our approach maintains accuracy levels while achieving over 70% reduction in inference cost, surpassing competitive baselines. Our framework provides a scalable, unsupervised solution for reliable and efficient LLM reasoning.