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Large Language Models (LLMs) have shown promising results in coreference resolution, especially after fine-tuning. However, recent generative approaches face a critical issue: hallucinations—where the model generates content not present in the original input. These hallucinations make evaluation difficult and decrease overall performance. To address this issue, we analyze the underlying causes of hallucinations and propose a low-hallucination and efficient solution. Specifically, we introduce Efficient Constrained Decoding for Coreference Resolution, which maintains strong robustness while significantly improving computational efficiency. On the English OntoNotes development set, our approach achieved slightly better performance than previous state-of-the-art methods, while requiring substantially fewer parameters.