  Two alternative scenarios are shown possible in Quantum Mechanics working
with non-Hermitian $PT-$symmetric form of observables. While, usually, people
assume that $P$ is a self-adjoint indefinite metric in Hilbert space (and that
their $P-$pseudo-Hermitian Hamiltonians $H$ possess the real spectra etc), we
propose to relax the constraint $P=P^\dagger$ as redundant. Non-Hermitian
triplet of coupled square wells is chosen for illustration purposes. Its
solutions are constructed and the observed degeneracy of their spectrum is
attributed to the characteristic nontrivial symmetry $S={P}^{-1} {P}^\dagger
\neq I$ of the model $H$. Due to the solvability of the model the determination
of the domain where the energies remain real is straightforward. A few remarks
on the correct (albeit ambiguous) physical interpretation of the model are
added.
