  In many PT symmetric models with real spectra, apparently, energy levels
"merge and disappear" at a point of the spontaneous PT-symmetry breaking. We
argue that such an oversimplified and discontinuous physical interpretation of
this mechanism as proposed, e.g., by one of us in Phys. Lett. A 285 (2001), p.
7 would be inappropriate. Using the elementary square-well model of the above
reference in the strongly non-Hermitian regime we exemplify how the doublets of
states with broken PT symmetry continue to exist at complex conjugate energies.
In contrast to many other exactly solvable examples of such a mechanism (we
listed some of them in quant-ph/0110064), our present model of symmetry
breaking does not complexify all the spectrum at once. "Realistically", it
rather proceeds step by step, starting from the low-lying part of the spectrum
and involving more and more excited states with an increasing degree of
non-Hermiticity of the underlying interaction.
