ABSTRACT We apply a synchrocurvature spectral emission model based on characterizing the dynamics of magnetospheric particles to fit the phase-average spectra of the most extended data base for the non-thermal spectra of pulsars. We consider 36 pulsars with well-determined non-thermal spectra from X-rays to gamma-rays. The sample includes Crab and the Crab twin, for which the spectra extend even to the optical/ultraviolet and infrared energies. We find that the model – with just three physical parameters and a global scaling – can fit the observations well across eight orders of magnitude for 18 of the 36 pulsars studied. Additionally, we find a set of eight pulsars for which the model still provides arguably good fits and another set of 10 pulsars for which the model fails in reproducing the spectra. We discuss why, propose and provide physical interpretations for a simple model extension (related to the geometry of the accelerating system with regards to the observer) that allows dealing with all such cases, ultimately providing very good fits for all pulsars. The extended model is still austere, adding only two additional parameters to the former set, of the same kind of the ones previously used. We use these fits to discuss issues going from the observed spectral origin, to the extent of the dominance of synchrotron or curvature regimes, the use of a model as predictor for searching new non-thermal pulsars starting from gamma-ray surveys, and how the model offers a setting where phase shifts between X-ray and gamma-ray light curves would naturally arise.