A fixed-mass multifractal (FMA) analysis was used to investigate natural river networks and braided channels. In particular, while the study of natural river networks was performed with fixed-size algorithms (FSAs) in the past, the analysis of natural braided channels was not pursued before to our knowledge. Results showed the multifractal and non-plane-filling nature of all the digitalized data sets. Analysis of the digitalization step (constant or not) was performed and showed that it does not exert a strong influence on the assessed values of the Lipschitz-Hölder exponents and the support dimensions, even if a constant step permits better reconstruction of the right sides of the spectra, for negative moment orders of probabilities. The FMA approach presented two improvements with respect to the FSA one, in terms of oscillations of the scaling curves for negative moment orders of probabilities and of error bars. A more precise assessment of the multifractal spectra is of great importance in the development of multifractal models for the simulation of flood hydrographs.