The cosmic-ray nuclei spectra feature breaks in their power-law shapes, with slight differences in the indices and in the break positions between the nuclei species. A model explaining these structural differences as propagation effects is presented, based on the hypothesis that the source spectrum from acceleration in supernova remnants is a common broken power law with exponential cut-off for all nuclei species. The observed structural differences in the spectra are instead attributed to soft breaks in the power-law rigidity dependence of the diffusion coefficient, as well as a spatial variation of the diffusion coefficient within the galaxy. Using a modified version of the numerical cosmic-ray propagation calculation code DRAGON and optimizing the model’s input parameters in a random walk, it is shown that such a model can, within experimental uncertainty, explain various nuclei spectra and primary-secondary ratios measurements by the ISS-based experiments CALET (Calorimetric Electron Telescope) and AMS-02 (Alpha Magnetic Spectrometer), as well as the CRS (Cosmic Ray Subsystem) on the Voyager space-probes.