There is no complete description of the emission physics during the prompt phase in gamma-ray bursts. Spectral analyses, however, indicate that many spectra are narrower than what is expected for nonthermal emission models. Here, we reanalyze the sample of 37 bursts in Yu et al. by fitting the narrowest time-resolved spectrum in each burst. We perform a model comparison between photospheric and synchrotron emission models based on Bayesian evidence. We compare the shapes of the narrowest expected spectra: emission from the photosphere in a non-dissipative flow and slow cooled synchrotron emission from a narrow electron distribution. We find that the photospheric spectral shape is preferred by 54% ± 8% of the spectra (20/37), while 38% ± 8% of the spectra (14/37) prefer the synchrotron spectral shape; three spectra are inconclusive. We hence conclude that GRB spectra are indeed very narrow and that more than half of the bursts have a photospheric emission episode. We also find that a third of all analyzed spectra, not only prefer, but are also compatible with a non-dissipative photosphere, confirming previous similar findings. Furthermore, we notice that the spectra that prefer the photospheric model all have low-energy power-law indices α gsim −0.5. This means that α is a good estimator for which model is preferred by the data. Finally, we argue that the spectra that statistically prefer the synchrotron model could equally as well be caused by subphotospheric dissipation. If that is the case, photospheric emission during the early, prompt phase would be even more dominant.