The Kepler mission observations, taken in the long cadence mode, have a time resolution of about 30 min. In this paper, we investigate how the long cadence binning influences the shapes of the light curves of eclipsing binaries. A simulated light curve of a contact binary exhibiting a flat-bottom secondary minimum was applied for this purpose. We found that the binning caused a change in the variation amplitude and the shape of the minima. We modelled the simulated light curves corresponding to periods between 0.2 and 2 d using a code that does not account for binning and we derived the parameters. It turned out that only when the binary period is close to or longer than about 1.5 d are the solutions derived with such a code accurate. Rigorous modelling of systems with shorter periods requires the use of codes that do account for phase smearing due to long exposure times. We selected a sample of contact binaries observed by the Kepler mission, exhibiting a flat-bottom secondary minimum and showing no intrinsic activity. We solved the light curves of the sample with the most recent (2015) version of the Wilson-Devinney code and we derived the system parameters. The best models that we derived indicate that most of the systems in our sample have a deep contact configuration and that 13 out of 17 required the addition of a third light for good fits. Our results suggest that 13 systems could have tertiary companions.