Large Reasoning Models (LRMs) have demonstrated remarkable capabilities by scaling up the length of Chain-of-Thought (CoT). However, excessively long reasoning traces pose substantial challenges for training cost and inference latency. While various CoT compression approaches have emerged to address this challenge, they face inherent trade-offs: token-level methods often disrupt syntactic and logical coherence, while step-level methods based on perplexity fail to reliably capture the logically critical reasoning steps because of the dilution of logical information. In this paper, we propose ASAP (Anchor-guided, SurprisAl-based Pruning), a novel coarse-to-fine framework for CoT compression. ASAP first performs anchor-guided pruning to preserve the core reasoning structure, which efficiently reduces the search space for subsequent processing. Leveraging the insight that logical branching choices are concentrated at the onset of reasoning steps, it then enables logic-aware pruning by selecting logically essential reasoning steps based on a novel first-token surprisal metric. Finally, ASAP distills these concise CoTs into target models so they can generate efficient reasoning traces at inference time. Experiments across math and code benchmarks show that ASAP preserves competitive accuracy while substantially reducing generated tokens, latency, and training cost, with additional validation on Qwen3 confirming its cross-model applicability.