Reference solutions and question-specific rubrics are not always available to guide the teacher in self-distillation. A large language model's own solution attempts offer an alternative, but their quality is difficult to assess in open-ended tasks without automatic correctness checks, and even correct attempts can involve uncertain token predictions. We propose Reliability--Uncertainty Self-Distillation (\method{}) to learn from these attempts. The same model serves as teacher and student: the teacher receives the question and completed attempt, and the student matches the teacher's token-level predictions using a question-only prompt. \method{} weights each attempt's distillation loss by additively combining judged reliability, estimated from a self-judge's score and confidence, with student predictive uncertainty. Across eleven reasoning benchmarks, \method{} outperforms all five baselines in average accuracy, reaching 70.47\% on Qwen3-4B and 76.69\% on Qwen3-8B (8.90 and 2.10 percentage points above the base models). Data and code are available at https://github.com/JP-25/RUSD.

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