Conceptual catchment models with more than four or five parameters calibrated to streamflow data often have poorly identified parameters. This study reassesses the role of the computationally efficient multinormal approximation to parameter uncertainty and considers the worth of multiresponse data to improve identifiability. A case study involving the nine-parameter CATPRO model presents three findings. First, when an overparameterized model is calibrated to streamflow data, the parameter covariance matrix can help identify the poorly defined parameters and provide insight about the structural reasons for poor identifiability. Second, when multiresponse data are available to calibrate the catchment model, the multinormal approximation may provide an adequate description of parameter uncertainty. Third, augmenting streamflow data with other response time series data may not reduce parameter uncertainty. Augmenting streamflow data with groundwater level data did little to reduce the uncertainty in the poorly defined CATPRO parameters, whereas augmenting with stream salinity data substantially reduced parameter uncertainty. This suggests the worth of multiresponse data should, where possible, be assessed a priori. ¿ 1998 American Geophysical Union