  Complex potential transformations which add imaginary parts to chosen energy
levels are given and qualitatively explained. Unexpected shape similarity of
potential perturbations for real and imaginary E-shifts of bound states are
exhibited. The imaginary E-shifts in the continuous spectrum lead to a
surprising quasi-periodic field raking up initial propagating waves into
localized states. Complex periodic potentials without lacunas (!) are
constructed. The fission of quasi-bound states when neighbour complex
eigenvalues approach one another is demonstrated. E-shift algorithms represent
wide classes of exactly solvable quantum models for non-self-adjoint operators.
