  The first and second-order supersymmetry transformations are used to generate
Hamiltonians with known spectra departing from the trigonometric Poschl-Teller
potentials. The several possibilities of manipulating the initial spectrum are
fully explored, and it is shown how to modify one or two levels, or even to
leave the spectrum unaffected. The behavior of the new potentials at the
boundaries of the domain is studied.
