We investigate the photoproduction off a proton target in the channel with K+ and Sigma(0) in the final state. The model of our choice for description of this process is based on effective Lagrangians at the tree level; it is the so-called isobar model. This formalism was developed previously for description of K(+)A photoproduction, and the aim of this study is to provide an extension of this description towards Sigma photoproduction channels. Our fitting strategy has two stages. In the first stage we employ standard chi(2) minimization using a set of resonances, based on previous works. In the second stage, we apply a model selection procedure to the same set of resonances using L-1 regularization in combination with criteria from information theory, and we obtain a sparser model. This gives us two fits which we compare with data and comment on their behavior. Some of the available data (CLAS differential cross sections at energies W > 2.4 GeV, SAPHIR differential cross sections, and C-x and C-z' polarizations) are not included in the fits, but are used to test the predictive power of the two models. The sparser model shows better agreement with the unfitted data compared to the full model.