  In this follow up of arXiv:1812.04663 we analyze the generalized CP
symmetries of the charged lepton mass matrix compatible with the complex
version of the Tri-Bi-Maximal (TBM) lepton mixing pattern. These symmetries are
used to `revamp' the simplest TBM \textit{Ansatz} in a systematic way. Our
generalized patterns share some of the attractive features of the original TBM
matrix and are consistent with current oscillation experiments. We also discuss
their phenomenological implications both for upcoming neutrino oscillation and
neutrinoless double beta decay experiments.
