  We revisit the BPS spectrum of the supersymmetric CP(N-1) two-dimensional
model with Z_N-symmetric twisted masses m_l (l=0,1, ..., N-1). A related issue
we address is that of the curves of marginal stability (CMS) in this theory.
Previous analyses were incomplete. We close the gap by exploiting a number of
consistency conditions. In particular, we amend the Dorey formula for the BPS
spectrum. Our analysis is based on the exact Veneziano--Yankielowicz-type
superpotential and on the strong-coupling spectrum of the theory found from the
mirror representation at small masses, |m_l| << \Lambda . We show that at weak
coupling the spectrum, with necessity, must include N-1 BPS towers of states,
instead of just one, as was thought before. Only one of the towers is seen in
the quasiclassical limit. We find the corresponding CMS for these towers, and
argue that in the large-N limit they become circles, filling out a band on the
plane of a single mass parameter of the model at hand. Inside the CMS, N-1
towers collapse into N stable states.
