  We deform the real potential of Poeschl and Teller by a shift of its
coordinate in imaginary direction. We show that the new model remains exactly
solvable. Its bound states are constructed in closed form. Wave functions are
complex and proportional to Jacobi polynomials. Some of them diverge in the
Hermitian limit. In contrast, all their energies prove real and
shift-independent. In this sense the lost Hermiticity of our family of
Hamiltonians seems replaced by their accidental PT symmetry.
