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Recent advances have explored visual token pruning to accelerate the inference of large vision-language models (LVLMs). However, existing methods often struggle to balance token importance and diversity: importance-based methods tend to retain redundant tokens, whereas diversity-based methods may overlook informative ones. This trade-off becomes especially problematic under high reduction ratios, where preserving only a small subset of visual tokens is critical. To address this issue, we propose ID-Selection, a simple yet effective token selection strategy for efficient LVLM inference. The key idea is to couple importance estimation with diversity-aware iterative selection: each token is first assigned an importance score, after which high-scoring tokens are selected one by one while the scores of similar tokens are progressively suppressed. In this way, ID-Selection preserves informative tokens while reducing redundancy in a unified selection process. Extensive experiments across 5 LVLM backbones and 16 main benchmarks demonstrate that ID-Selection consistently achieves superior performance and efficiency, especially under extreme pruning ratios. For example, on LLaVA-1.5-7B, ID-Selection prunes 97.2% of visual tokens, retaining only 16 tokens, while reducing inference FLOPs by over 97% and preserving 91.8% of the original performance, all without additional training.