  We examine resonances for two systems consisting of a particle coupled to a
massless boson's field. The field is the free field in the whole space. In the
first system, the particle is confined inside a ball. We show that besides the
usual energy levels of the particle, which have become complex through the
coupling to the field, other resonances are to be taken into account if the
ball's radius is comparable to the particle's Compton wavelength. In the second
system, the particle is in a finite-depth square-well potential. We study the
way the resonances' width depends on the extent of the uncoupled particle's
wave functions. In both cases, we limit ourselves to considering two levels of
the particle only.
