Long chain-of-thought (Long-CoT) reasoning models have motivated a growing body of work on compressing reasoning traces to reduce inference cost, yet existing evaluations focus almost exclusively on task accuracy and token savings. Trustworthiness properties, whether acquired or reinforced through post-training, are encoded in the same parameter space that compression modifies. This means preserving accuracy does not, a priori, guarantee preserving trustworthiness. We conduct the first systematic empirical study of how CoT compression affects model trustworthiness, evaluating multiple models of different scales along three dimensions: safety, hallucination resistance, and multilingual robustness. Under controlled comparisons, we find that CoT compression frequently introduces trustworthiness regressions and that different methods exhibit markedly different degradation profiles across dimensions. To enable fair comparison across bases, we propose a normalized efficiency score for each dimension that reveals how naïve scalar metrics can obscure trustworthiness trade-offs. As an existence proof, we further introduce an alignment-aware DPO variant that reduces CoT length by 19.3\% on reasoning benchmarks with substantially smaller trustworthiness loss. Our findings suggest that CoT compression should be optimized not only for efficiency but also for trustworthiness, treating both as equally important design constraints.

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