  In paper approach of double complex SUSY-transformations with not coincident
complex energies of transformation is developed, allowing to deform given real
potential $V_{1}$ with obtaining exact solutions. The explicit solutions of the
deformation of shape of the potential, its wave function at arbitrary energy,
not coincident with energies of transformation, wave functions at the energies
of transformation are obtained, condition of keeping of continuity of the
solutions and isospectral condition are determined. Using a rectangular well of
finite width with infinitely high walls as the starting $V_{1}$ with discrete
energy spectrum, by the proposed approach new types of deformation of this
potential with deformation of the energy spectrum as a whole have been
obtained. The new potential contains the rectangular well as own partial case
(with simultaneous transformation of the shape of this new potential, energy
spectrum, wave functions of all bound states, wave function at arbitrary energy
into corresponding characteristics of the rectangular well at needed choice of
parameters). Using null potential as the starting $V_{1}$ with continuous
energy spectrum, new form of reflectionless real potential has been
constructed. This potential generalizes well-known reflectionless potential of
the type $V_{\rm ref}(x) = A^{2}(1-2 {\rm sech}^{2}{Ax})$, allowing: to pull
down tails of the potential $V_{\rm ref}$ in the asymptotic regions up to zero
(with keeping of nonzero depth); to pull down continuously the depth of the
hole; to displace arbitrary along axis $x$ the hole with its passing through
zero; to create and to increase the second hole, transforming $V_{\rm ref}$
into double-well potential; to control continuously and simply the asymmetry of
the shape of such reflectionless potential.
