  We discussed twisted quantum deformations of D=4 Lorentz and Poincare
algebras. In the case of Poincare algebra it is shown that almost all classical
r-matrices of S.Zakrzewski classification can be presented as a sum of
subordinated r-matrices of Abelian and Jordanian types. Corresponding twists
describing quantum deformations are obtained in explicit form. This work is an
extended version of the paper \url{arXiv:0704.0081v1 [math.QA]}.
