A promising approach for multi-microphone speech separation involves two deep neural networks (DNN), where the predicted target speech from the first DNN is used to compute signal statistics for time-invariant minimum variance distortionless response (MVDR) beamforming, and the MVDR result is then used as extra features for the second DNN to predict target speech. Previous studies suggested that the MVDR result can provide complementary information for the second DNN to better predict target speech. However, on fixed-geometry arrays, both DNNs can take in, for example, the real and imaginary (RI) components of the multi-channel mixture as features to leverage the spatial and spectral information for enhancement. It is not explained clearly why the linear MVDR result can be complementary and why it is still needed, considering that the DNNs and the beamformer use the same input, and the DNNs perform non-linear filtering and could render the linear filtering of MVDR unnecessary. Similarly, in monaural cases, one can replace the MVDR beamformer with a monaural weighted prediction error (WPE) filter. Although the linear WPE filter and the DNNs use the same mixture RI components as input, the WPE result is found to significantly improve the second DNN. This study provides a novel explanation from the perspective of the low-distortion nature of such algorithms, and finds that they can consistently improve phase estimation. Equipped with this understanding, we investigate several low-distortion target estimation algorithms including several beamformers, WPE, forward convolutive prediction, and their combinations, and use their results as extra features to train the second network to achieve better enhancement. Evaluation results on single- and multi-microphone speech dereverberation and enhancement tasks indicate the effectiveness of the proposed approach, and the validity of the proposed view.