We consider the different approximations for the bandgap renormalization (BGR) within the random phase approximation (RPA), the quasi-static limit and the plasmon-pole approximation, and compare with the full result. We then include bulk optical phonons and also the phonon confinement using the phonons from the dielectric continuum (DC) model. We show that the results are very similar except at low densities where the quasi-static results overestimate the renormalization.