Dual-tree wavelet transforms have recently gained popular- ity [1] since they provide low-redundancy directional anal- yses of images. In our recent work, dyadic real dual-tree decompositions have been extended to the M-band case, so adding much flexibility to this analysis tool. In this work, we propose to further extend this framework on two fronts by considering (i) biorthogonal and (ii) complex M-band dual- tree decompositions. Denoising results are finally provided to demonstrate the validity of the proposed design rules.