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 non-thermal emission models . Here , we reanalyse the sample of 37 bursts in \citet Yu2019 , by fitting the narrowest time-resolved spectrum in each burst . We perform model comparison between a photospheric and a synchrotron emission model based on Bayesian evidence . We choose to compare the shape 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 \pm 8 \% of the spectra ( 20/37 ) , while 38 \pm 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 analysed 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 a low-energy power-law indices \alpha \ga - 0.5 . This means that \alpha is a good estimator of which model is preferred by the data . Finally , we argue that the spectra which statistically prefer the synchrotron model , could equally well be caused by subphotospheric dissipation . If that is the case , photospheric emission during the early , prompt phase would be even more dominant .