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As large language models are increasingly deployed as personal agents handling sensitive workflows, adhering to CI becomes critical. However, even frontier models remain unreliable in making disclosure decisions, and existing mitigation strategies often degrade underlying task performance. To overcome this privacy-utility trade-off, we propose SELFCI, a complementary self-distillation framework that decouples information suppression from task resolution. SELFCI jointly optimizes two independent reverse KL divergences over distinct teacher distributions derived from feedback: one encourages preserving task-relevant information for utility, while the other enforces minimal and appropriate disclosure. 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SELFCI jointly optimizes two independent reverse KL divergences over distinct teacher distributions derived from feedback: one encourages preserving task-relevant information for utility, while the other enforces minimal and appropriate disclosure. 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