Chain-of-Thought (CoT) distillation transfers multi-step reasoning from large reasoning models to smaller students, but verbose teacher traces inflate both training and inference cost. Existing CoT compression methods fall into two families, selective pruning and generative rewriting, yet prior studies have left key factors entangled: granularity is confounded with importance criteria in pruning, restructuring level is rarely isolated in rewriting, and compression budgets are not systematically evaluated across domains or regimes. We recast CoT compression along three dimensions: importance criterion, restructuring level, and compression budget. Sweeping these across two model families, Math and General domains, and Long-/Short-CoT regimes, we find that (i) importance criterion utility is strictly governed by granularity: step-level criteria converge on a shared reasoning backbone, while token-level pruning requires symbol-aware signals to preserve the logical core; (ii) restructuring level inverts across domains: Math degrades monotonically with structural disruption, while aggressive rewriting acts as a denoiser on General tasks; (iii) training-time compression does not necessarily translate to inference-time savings: Long-CoT students retain verbose habits despite concise supervision, making the training ratio an optimistic lower bound on deployment cost. These findings yield condition-aware guidelines for matching compression to deployment context.

Large Language Models (LLMs) excel in reasoning tasks through Chain-of-Thought (CoT) prompting. However, CoT prompting greatly increases computational demands, which has prompted growing interest in distilling CoT capabilities into Small Language Models (SLMs). This study systematically examines the factors influencing CoT distillation, including the choice of granularity, format and teacher model. Through experiments involving four teacher models and seven student models across seven mathematical and commonsense reasoning datasets, we uncover three key findings: (1) Unlike LLMs, SLMs exhibit a non-monotonic relationship with granularity, with stronger models benefiting from finer-grained reasoning and weaker models performing better with simpler CoT supervision; (2) CoT format significantly impacts LLMs but has minimal effect on SLMs, likely due to their reliance on supervised fine-tuning rather than pretraining preferences; (3) Stronger teacher models do NOT always produce better student models, as diversity and complexity in CoT supervision can outweigh accuracy alone. These findings emphasize the need to tailor CoT strategies to specific student model, offering actionable insights for optimizing CoT distillation in SLMs.