We discuss spontaneously broken CP symmetry in two right-handed neutrino
models based on the idea of having a {\it different residual flavour symmetry},
together with a {\it different residual CP symmetry}, associated with each of
the two right-handed neutrinos. The charged lepton sector also has a {\it
different residual flavour symmetry}. In such a {\it tri-direct CP approach},
we show that the combination of the three residual flavour and two residual CP
symmetries provides a new way of fixing the parameters. To illustrate the
approach, we revisit the Littlest Seesaw (LSS) model based on S4β and then
propose new variants which have not so far appeared in the literature, with
different predictions for each variant. We analyse numerically the predictions
of the new variants, and then propose an explicit model which can realise one
of the successful benchmark points, based on the atmospheric flavon vacuum
alignment (1,Ο2,Ο) and the solar flavon vacuum alignment (1,β7/2,β7/2).Comment: 31 pages, 4 figure
