  The spectrum of complex PT-symmetric potential, $V(x)=igx$, is known to be
null. We enclose this potential in a hard-box: $V(|x| \ge 1) =\infty $ and in a
soft-box: $V(|x|\ge 1)=0$. In the former case, we find real discrete spectrum
and the exceptional points of the potential. The asymptotic eigenvalues behave
as $E_n \sim n^2.$ The solvable purely imaginary PT-symmetric potentials
vanishing asymptotically known so far do not have real discrete spectrum. Our
solvable soft-box potential possesses two real negative discrete eigenvalues if
$|g|<(1.22330447)$. The soft-box potential turns out to be a scattering
potential not possessing reflectionless states.
