Some Feynman-diagram models of Regge poles are used to study daughter trajectories of bosons in scalar-meson-scalar-meson scattering. Both the simple model with bare propagators and a generalized model that includes propagator self-energy insertions are considered. It is found that, in the simple model, the second daughter is a fixed (as a function of the squared momentum transfer t) double pole in complex J plane. When self-energy corrections to the propagator are included, the fixed double pole breaks up into a moving daughter trajectory and a moving companion trajectory. It is found that away from t=0, the daughter and companion trajectories get mixed up in a complicated and model-dependent manner.