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• Guidelines for the use of snow data combined with runoff to calibrate models. • Improvement of the snow simulations without impairing runoff performance. • The improvement in the model consistency is not accompanied by lower equifinality. • Using snow data does not improve model robustness to climate variability. This paper compares different calibration strategies for using snow data combined with streamflow records to constrain model optimisation in mountain catchments. In particular, it assesses to what extent the use of snow observations makes it possible to improve the consistency, identifiability and robustness of the calibrated parameters. To answer this question, a semi-distributed snow and ice model was used on top of a rainfall-runoff model using the SAFRAN meteorological reanalysis as input dataset on several catchments in the Alps and Pyrenees. Model calibration and control were based on streamflow observations, remotely-sensed snow-covered areas and in-situ snow water equivalent (SWE) measurements. The snow and rainfall-runoff parameters were calibrated sequentially and simultaneously against objective functions integrating different combinations of runoff, snow cover and SWE criteria. Statistical assessment of model performances in independent evaluation periods showed that sequential calibration of the snow parameters gives too much weight to snow compared to runoff. Instead, incorporating snow data in the simultaneous calibration of the parameters improves snow simulations without impairing runoff performance. This can be achieved by limiting the weight of the snow criteria to 25% in the objective function. Although local SWE measurements were found to be more useful than satellite observations for identifying more consistent parameters, it is advisable to include both in the calibration process through a compromise objective function. However, the improved model consistency was not accompanied by a significant reduction in equifinality and optimisation times. On the other hand, improving internal consistency made it possible to reduce the interdependence between the parameters of the snow model and those of the rainfall-runoff model. This also made it possible to identify the least sensitive snow parameters in order to fix them at general values without impairing model performance while reducing equifinality with a more parsimonious model. Finally, there was no evidence that using snow observations in the calibration process improves model robustness with respect to climate variability. [ABSTRACT FROM AUTHOR]