The phonon sideband spectrum of bound excitons in N-doped GaP is calculated using a model wherein intrinsic lattice phonons assist momentum conservation through indirect electron-hole recombination at the impurity site. Detailed comparisons are made of the spectrum obtained on the basis of this model and the experimental spectrum. These comparisons are used to demonstrate that near-resonant processes strongly affect the phonon-assisted indirect recombination and thus that such processes are important in the determination of the shape of the phonon sideband spectrum. Using this phonon sideband theory, two models for the N-impurity wave function are tested by comparing the sideband spectra calculated using these models with the experimental spectrum. Finally, by including a configuration-coordinate-type coupling for the optic phonons, it is demonstrated that some of the low-energy structure observed in the luminescence spectrum can be interpreted as replicas of the spectrum described by the indirect transition model.