ABSTRACT The detected high-energy pulsars’ population is growing in number, and thus, having agile and physically relevant codes to analyse it consistently is important. Here, we update our existing synchro-curvature radiation model by including a better treatment of the particle injection, particularly where the large pitch angle particles dominate the spectra, and by implementing a fast and accurate minimization technique. The latter allows a large improvement in computational cost, needed to test model enhancements, and to apply the model to a larger pulsar population. We successfully fit the sample of pulsars with X-ray and gamma-ray data. Our results indicate that, for every emitting particle, the spatial extent of their trajectory where the pitch angle is large and most of the detected X-ray radiation is produced is a small fraction of the light cylinder. We also confirm with this new approach that synchrotron radiation is not negligible for most of the gamma-ray pulsars detected. In addition, with the results obtained, we argue that J0357+3205 and J2055+2539 are MeV pulsar candidates and are suggested for exhaustive observations in this energy band.