We introduce ClaimCheck, an efficient fact-checking system that verifies textual claims using smaller, open-source large language models. ClaimCheck integrates two fact-checking strategies, claim-matching and novel claim processing. Claim-matching uses related fact-checks from trusted organizations to fact-check a claim. Novel claim processing breaks down fact-checking into manageable subtasks—generating targeted questions, retrieving Web evidence, extracting answers, and synthesizing verdicts. Evaluation on the AVeriTeC benchmark demonstrates 62.6% verdict prediction accuracy, with claim-matching providing a 2.8% improvement. ClaimCheck approaches the performance of state-of-the-art systems while requiring significantly fewer computational resources, demonstrating the effectiveness of using small language models for fact-checking tasks. Furthermore, our code is publicly available to help make automated fact-checking more accessible.