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This paper proposes a noise-robust speech recognition method composed of weak noise suppression (NS) and weak Vector Taylor Series Adaptation (VTSA). The proposed method compensates defects of NS and VTSA, and gains only the advantages by them. The weak NS reduces distortion by over-suppression that may accompany noise-suppressed speech. The weak VTSA avoids over-adaptation by offsetting a part of acoustic-model adaptation that corresponds to the suppressed noise. Evaluation results with the AURORA2 database show that the proposed method achieves as much as 1.2 points higher word accuracy (87.4%) than a method with VTSA alone (86.2%) that is always better than its counterpart with NS.