The speech distortion weighted multi-channel Wiener filter (SDW-MWF) is considered to control the tradeoff between noise reduction and speech distortion. In a single target speech source, speech correlation matrix can be assumed to be rank-1 in the implementation of the SDW-MWF. We evaluate the rank-1 SDW-MWF as a pre-processor of speech recognizer and discuss regarding optimal distortion weight. We also propose a modified SDW-MWF providing a full range control of speech distortion as well as outperforming the rank-1 SDW-MWF. The experimental results show that aggressive noise reduction strategy is preferable for maximizing the performance of speech recognizer. The results also show that the proposed filter performs better than the conventional rank-1 SDW-MWF.