Hydrological modelling of glacierized catchments is challenging because internal inconsistencies might be hidden due to ice melt which represents an additional source of water. This is even more significant if there are no data available to evaluate model simulations, as is often the case in remote areas. On the other hand, these glacierized catchments are important source regions for water, and detailed knowledge of water availability is a prerequisite for good resource management strategies. An important question is how useful a limited amount of data might be for model applications. Therefore, in this study the predictive power of limited discharge measurements, mass balance observations and the combination of both was analyzed by means of Monte Carlo analyses with multi-criteria model performance evaluation. Ensembles of 100 parameter sets were selected by evaluating the simulations based on a limited number of discharge measurements, glacier mass balance, and the combination of discharge and mass balance observations. Then the ensemble simulation of runoff was evaluated for the entire runoff series. The result indicated that a single annual glacier mass balance observation contained useful information to constrain hydrological models. Combining mass balance observations with a few discharge data improved the internal consistency and significantly reduced the uncertainties compared to parameter set selections based on discharge measurements alone. To obtain good ensemble predictions, information on discharge was required for at least 3 days during the melting season. This demonstrated that the timing of runoff measurements is important for the information contained in these data.