Regularized acoustic multi-channel equalization techniques, such as regularized partial multi-channel equalization based on the multiple-input/output inverse theorem (RPMINT), are able to achieve a high dereverberation performance in the presence of room impulse response perturbations but may lead to amplification of the additive noise. In this paper, two time-domain techniques aiming at joint dereverberation and noise reduction based on acoustic multi-channel equalization are proposed. The first technique, namely RPMINT for joint dereverberation and noise reduction (RPM-DNR), extends RPMINT by explicitly taking the noise statistics into account. In addition to the regularization parameter used in RPMINT, the RPM-DNR technique introduces an additional weighting parameter, enabling a trade-off between dereverberation and noise reduction. The second technique, namely multi-channel Wiener filter for joint dereverberation and noise reduction (MWF-DNR), takes both the speech and the noise statistics into account and uses the RPMINT filter to compute a dereverberated reference signal for the multi-channel Wiener filter. The MWF-DNR technique also introduces an additional weighting parameter, which now provides a trade-off between speech distortion and noise reduction. To automatically select the regularization and weighting parameters, for the RPM-DNR technique a novel procedure based on the L-hypersurface is proposed, whereas for the MWF-DNR technique two decoupled optimization procedures based on the L-curve are used. Extensive simulations demonstrate using instrumental measures that the RPM-DNR technique maintains the dereverberation performance of the RPMINT technique while improving its noise reduction performance. Furthermore, it is shown that the MWF-DNR technique yields a significantly better noise reduction performance than the RPM-DNR technique at the expense of a worse dereverberation performance.