  We continue to study the BPS spectrum of the N=(2,2) CP(N-1) model with the
Z_N-symmetric twisted mass terms. We focus on analysis of the "extra" towers
found previously in [1], and compare them to the states that can be identified
in the quasiclassical domain. Exact analysis of the strong-coupling states
shows that not all of them survive when passing to the weak-coupling domain.
Some of the states decay on the curves of the marginal stability (CMS). Thus,
not all strong-coupling states can be analytically continued to weak coupling
to match the observable bound states.
  At weak coupling, we confirm the existence of bound states of
topologically-charged kinks and elementary quanta. Quantization of the U(1)
kink modulus leads to formation of towers of such states. For the Z_N-symmetric
twisted masses their number is by far less than N-1 as was conjectured
previously. We investigate the quasiclassical limit and show that out of N
possible towers only two survive in the spectrum for odd N, and a single tower
for even N. In the case of CP^2 theory the related CMS are discussed in detail.
In these points we overlap and completely agree with the results of Dorey and
Petunin. We also comment on 2D-4D correspondence.
