Large language models often answer from knowledge learned during training, even when a provided passage contradicts that knowledge. To address this problem, contrastive decoding contrasts the predictions under the full and a modified prompt at every token, but it also alters correct answers that the passage supports. We show that checking answers against the passage removes this trade-off. Based on this observation, we propose Accept-or-Repair (AoR), a training-free procedure. AoR keeps a sampled answer if the passage supports it. Otherwise, it tries up to two replacements with contrastive decoding, returning one as soon as it passes this check. It rejects replacements that repeat the answer generated without the passage when the passage favors another answer. Our experiments show that AoR raises the score over sampling by 12.5 points on counterfactual passages and 2.3 on ordinary ones, surpassing eight contrastive and prompting baselines on both, including when each receives the same rejection rule. Replacing only initial answers that the passage does not support improves the average score of every decoder. These results suggest that models can follow passages that contradict their knowledge while preserving accuracy on passages that agree with it. Code will be released at https://github.com/js-lee-AI/AoR.

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