The Large Area Telescope onboard Fermi has discovered more than two hundred gamma-ray pulsars. But only eight have pulsations detected also at hard X-ray energies. Enlarging the X-ray-detected gamma-ray pulsars is essential to understand what are the control parameters behind the observed phenomenology. Using a theoretical model we recently developed, we have fitted all known spectra of gamma-ray pulsars and obtained estimates for their flux levels in X-rays. Based on the success of the model, we could enlarge the sample of non-thermal X-ray detected pulsars.