  Many indefinite-metric (often called pseudo-Hermitian or PT-symmetric)
quantum models H prove "physical" (i.e., Hermitian with respect to an
innovated, ad hoc scalar product) inside a characteristic domain of parameters
D. This means that the energies get complex (= unobservable) beyond the
boundary (= Kato's "exceptional points", EPs). In a solvable example we detect
an enlargement of D caused by the emergence of a new degree of freedom. We
conjecture that such a beneficial mechanism of a return to the real spectrum
near EPs may be generic and largely model-independent.
