Physically based hydrological models describe natural processes more accurately than conceptual models but require extensive data sets to produce accurate results. To identify the value of different data sets for improving the performance of the distributed hydrological model TOPKAPI we combine a multivariable validation technique with Monte Carlo simulations. The study is carried out in the snow and ice-dominated Rhonegletscher basin, as these types of mountainous basins are generally the most critical with respect to data availability and sensitivity to climate fluctuations. Each observational data set is used individually and in combination with the other data sets to determine a subset of best parameter combinations out of 10,000 Monte Carlos runs performed with randomly generated parameter sets. We validate model results against discharge, glacier mass balance, and satellite snow cover images for a 14 year time period (1994-2007). While the use of all data sets combined provides the best overall model performance (defined by the concurrent best agreement of simulated discharge, snow cover and mass balance with their respective measurements), the use of one or two variables for constraining the model results in poorer performance. Using only one data set for constraining the model glacier mass balance proved to be the most efficient observation leading to the best overall model performance. Our main result is that a combination of discharge and satellite snow cover images is best for improving model performance, since the volumetric information of discharge data and the spatial information of snow cover images are complementary.