In a Monte-Carlo Hauser-Feshbach statistical framework, we describe spectra, average multiplicities, average energy and multiplicity distributions of the prompt γ rays produced in the thermal neutron-induced fission of 235 U and 239 Pu, and the spontaneous fission of 252 Cf. Comparisons against recent experimental data show reasonable agreement in all cases investigated, after adjustment of the initial spin distribution in the fission fragments. In particular, when we include in the calculation the Doppler broadening we obtain a qualitatively good description of the measured low-energy spectra, where contributions from collective discrete transitions in specific fragments can be identified. At higher energies, both the calculated neutron and γ-ray spectra are softer than experimental data. The impact of selected model parameters on the prompt neutron and γ-ray spectra is analyzed. Finally, we present prompt γ spectrum and multiplicity distribution for the neutron-induced fission of 235 U for 5.5 MeV neutron incident energy, just below the threshold for second-chance fission.