  The confluent second-order supersymmetric quantum mechanics, in which the
factorization energies tend to a common value, is used to generate Hamiltonians
with known spectra departing from the hyperbolic Rosen-Morse and Eckart
potentials. The possible spectral modifications, as to create a new level or to
delete a given one, as well as the isospectral transformations, are discussed.
