Applying hydrological models for river basin management depends on the availability of the relevant data information to constrain the model residuals. The estimation of reliable parameter values for parameterized models is not guaranteed. Identification of influential model parameters controlling the model response variations either by main or interaction effects is therefore critical for minimizing model parametric dimensions and limiting prediction uncertainty. In this study, the Sobol variance-based sensitivity analysis method was applied to quantify the importance of the HBV conceptual hydrological model parameterization. The analysis was also supplemented by the generalized sensitivity analysis method to assess relative model parameter sensitivities in cases of negative Sobol sensitivity index computations. The study was applied to simulate runoff responses at twelve catchments varying in size. The result showed that varying up to a minimum of four to six influential model parameters for high flow conditions, and up to a minimum of six influential model parameters for low flow conditions can sufficiently capture the catchments' responses characteristics. To the contrary, varying more than nine out of 15 model parameters will not make substantial model performance changes on any of the case studies.