Large language models (LLMs) have achieved remarkable advancements in the field of natural language processing. However, the sheer scale and computational demands of these models present formidable challenges when considering their practical deployment in resource-constrained contexts. While techniques such as chain-of-thought (CoT) distillation have displayed promise in distilling LLMs into small language models (SLMs), there is a risk that distilled SLMs may still carry over flawed reasoning or hallucinations inherited from their LLM counterparts. To address these issues, we propose a twofold methodology: First, we introduce a novel method for distilling the self-evaluation capability inherent in LLMs into SLMs, which aims to mitigate the adverse effects of erroneous reasoning and reduce hallucinations. Second, we advocate for a comprehensive distillation process that incorporates multiple distinct chain-of-thought and self-evaluation paradigms and ensures a more holistic and robust knowledge transfer into SLMs. Experiments on three NLP benchmarks demonstrate that our method significantly improves the performance of distilled SLMs and sheds light on the path towards developing smaller models closely aligned with human cognition.