The origin of the prompt emission in gamma-ray bursts (GRBs) is still an unsolved problem and several different mechanisms have been suggested. Here, we fit Fermi GRB data with a photospheric emission model which includes dissipation of the jet kinetic energy below the photosphere. The resulting spectra are dominated by Comptonization and contain no significant contribution from synchrotron radiation. In order to fit to the data, we span a physically motivated part of the model's parameter space and create DREAM (Dissipation with Radiative Emission as A table Model), a table model for XSPEC. We show that this model can describe different kinds of GRB spectra, including GRB 090618, representing a typical Band function spectrum, and GRB 100724B, illustrating a double peaked spectrum, previously fitted with a Band+blackbody model, suggesting they originate from a similar scenario. We suggest that the main difference between these two types of bursts is the optical depth at the dissipation site.