Conceptual hydrological modelling has under-utilised classical parameter analysis techniques (for both optimisation and uncertainty assessment) due to the prohibitively complicated nonsmooth geometry of typical parameter distributions. In the companion paper, a numerically robust model implementation framework was developed, based on stable time stepping schemes and careful threshold smoothing to eliminate the roughness of parameter surfaces. Here, this framework is exploited to enable parameter estimation using powerful and well-established techniques including: (i) Newton-type optimisation and (ii) principal-component-type (Hessian-based) uncertainty analysis. A case study using a representative rainfall-runoff-snow model illustrates the advantages of these previously unavailable methods, contrasting them with slower and less informative current approaches designed for nonsmooth functions. In addition to boosting the computational efficiency, the methods advocated in the paper yield more insight into improved model formulation and parameterisation (e.g., reducing model nonlinearity, detecting ill-conditioning and handling parameter multi-optimality). The impact of extreme model nonlinearity on model and parameter stability is also discussed, focusing on model identification aspects.