Pseudo-Hermiticity, weak pseudo-Hermiticity and eta-orthogonality condition

We discuss certain features of pseudo-Hermiticity and weak pseudo-Hermiticity conditions and point out that, contrary to a recent claim, there is no inconsistency if the correct orthogonality condition is used for the class of pseudo-Hermitian, PT-symmetric Hamiltonians of the type $H_{\beta} = [p + {\rm i} \beta \nu(x)]^2/2m + V(x)$.