[en] To determine the Hilbert space and inner product for a quantum theory defined by a non-Hermitian PT-symmetric Hamiltonian H, it is necessary to construct a new time-independent observable operator called C. It has recently been shown that for the cubic PT-symmetric Hamiltonian H=p²+x²+iεx³ one can obtain C as a perturbation expansion in powers of ε. This Letter considers the more difficult case of noncubic Hamiltonians of the form H=p²+x²(ix)^δ (δ≥0). For these Hamiltonians it is shown how to calculate C by using nonperturbative semiclassical methods