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Task-agnostic prompt compression leverages the redundancy in natural language to reduce computational overhead and enhance information density within prompts, especially in long-context scenarios. Existing methods predominantly rely on information entropy as the metric to compress lexical units, aiming to achieve minimal information loss. However, these approaches overlook two critical aspects: (i) the importance of attention-critical tokens at the algorithmic level, and (ii) shifts in information entropy during the compression process. Motivated by these challenges, we propose a dynamic attention-aware approach for task-agnostic prompt compression (DAC). This approach effectively integrates entropy and attention information, dynamically sensing entropy shifts during compression to achieve fine-grained prompt compression. Extensive experiments across various domains, including LongBench, GSM8K, and BBH, show that DAC consistently yields robust and substantial improvements across a diverse range of tasks and LLMs, offering compelling evidence of its efficacy.