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Cognitive Restructuring (CR) uses multi-turn dialogue to identify and restructure one’s negative thoughts, arising from mental health issues, into more helpful and positive ones. Clinician shortage and stigma urge the development of human-LLM interactive psychotherapy for CR. Yet, effectively implementing CR is hindered by entrenched cognitive distortions, emotional resistance, and individual differences, which existing works have not overcome. To bridge this gap, we propose CRDial, a novel framework that structures CR as theory-grounded multi-stage multi-turn dialogue, integrating multi-aspect supportive strategies for emotional management and a multi-channel loop mechanism to account for diverse individual distortions. With CRDial, we distill Crisp, a large-scale and high-quality bilingual dialogue dataset, from LLM. We then train Crispers, Crisp-based conversational LLMs for CR, at 7B and 14B scales. Extensive human studies show the superiority of Crispers in pointwise, pairwise, and intervention evaluations.