Discharge data used to calibrate and evaluate hydrological models can be highly uncertain and this uncertainty affects the conclusions that we can draw from modelling results. We investigated the role of discharge data uncertainty and its representation in hydrological model calibration to give recommendations on methods to account for data uncertainty. We tested five different representations of discharge data uncertainty in calibrating the HBV-model for three Swiss catchments, ranging from using no information to using full empirical probability distributions for each time step. We developed a new objective function to include discharge data uncertainty, as quantified by these distributions directly in calibration to hydrological time series. This new objective function provided more reliable results than using no data uncertainty or multiple realizations of discharge time series. We recommend using the new objective function in combination with empirical or triangular distributions of the discharge data uncertainty.