  Salpeter equations with potential functions rising to infinity in
configuration space do not automatically predict stable bound states. For this
to happen, also the Lorentz behaviour of the involved Bethe-Salpeter kernels is
crucial. At least for interaction potentials of harmonic-oscillator form
analytic scrutinies of Salpeter equations with confining interactions may
identify those Bethe-Salpeter kernels which describe bound states free from the
notorious instabilities encountered in numerical evaluations. Such truly
confining kernels can be singled out systematically by requesting the resulting
bound-state energy spectra to be both real and discrete.
