  The metric associated with a quasi-Hermitian Hamiltonian and its physical
implications are scrutinised. Consequences of the non-uniqueness such as the
question of the probability interpretation and the possible and forbidden
choices of additional observables are investigated and exemplified by specific
illustrative examples. In particular it is argued that the improper
identification of observables lies at the origin of the claimed violation of
the brachistchrone transition time between orthogonal states. The need for
further physical input to remove ambiguities is pointed out.
