We point out that PT-symmetric potentials V$_{PT}$(x) having imaginary asymptotic saturation, V$_{PT}$(x = ±∞) = ±iV$_1$, V$_1$ ∈$ \mathbb{R}$ are devoid of scattering states and spectral singularity. We show the existence of real (positive and negative) discrete spectrum both with and without complex conjugate pair(s) of eigenvalues (CCPEs). If the eigenstates are arranged in the ascending order of the real part of the discrete eigenvalues, the initial states have few nodes but latter ones oscillate fast. Both real and imaginary parts of ψn(x) vanish asymptotically, and|ψn(x)| are nodeless. For the CCPEs, these are asymmetric and peaking on the left (right) and for real energies these are symmetric and peaking at the origin. For CCPEs E$_{±}$, the eigenstates ψ± follow the interesting property, |ψ+(x)| = N|ψ−(−x)|, N ∈ $ \mathbb{R$^+$}