Current RAG retrievers are designed primarily for human readers, emphasizing complete, readable, and coherent paragraphs. However, Large Language Models (LLMs) benefit more from precise, compact, and well-structured input, which enhances reasoning quality and efficiency. Existing methods rely on reranking or summarization to identify key sentences, but may introduce semantic breaks and unfaithfulness. Thus, efficiently extracting and organizing answer-relevant clues from large-scale documents while reducing LLM reasoning costs remains challenging in RAG systems. Inspired by Occam's razor, we frame LLM-centric retrieval as MinMax optimization: maximizing the extraction of potential clues and reranking them for well-organization, while minimizing reasoning costs by truncating to the smallest sufficient set of clues. In this paper, we propose CompSelect, a compact clue selection mechanism for LLM-centric RAG, consisting of a clue extractor, a reranker, and a truncator. (1) The clue extractor first uses answer-containing sentences as fine-tuning targets, aiming to extract sufficient potential clues; (2) The reranker is trained to prioritize effective clues based on real LLM feedback; (3) The truncator uses the truncated text containing the minimum sufficient clues for answering the question as fine-tuning targets, thereby enabling efficient RAG reasoning. Experiments on three QA datasets demonstrate that CompSelect improves performance while reducing both total and online latency compared to a range of baseline methods. Further analysis also confirms its robustness to unreliable retrieval and generalization across different scenarios.