Knowledge-intensive multi-hop question answering (QA) tasks, which require integrating evidence from multiple sources to address complex queries, often necessitate multiple rounds of retrieval and iterative generation by large language models (LLMs). However, incorporating many documents and extended contexts poses challenges -such as hallucinations and semantic drift-for lightweight LLMs with fewer parameters. This work proposes a novel framework called DEC (Dynamic Enhancement Chain). DEC first decomposes complex questions into logically coherent subquestions to form a hallucination-free reasoning chain. It then iteratively refines these subquestions through context-aware rewriting to generate effective query formulations. For retrieval, we introduce a lightweight discriminative keyword extraction module that leverages extracted keywords to achieve targeted, precise document recall with relatively low computational overhead. Extensive experiments on three multi-hop QA datasets demonstrate that DEC performs on par with or surpasses state-of-the-art benchmarks while significantly reducing token consumption. Notably, our approach attains state-of-the-art results on models with 8B parameters, showcasing its effectiveness in various scenarios, particularly in resource-constrained environments.