Two tube-based molecular models, the hierarchical 3.0 model and the branch-on-branch model were evaluated for their abilities to predict the behavior of a series of polydisperse, H-shaped, 1,4-polybutadienes. The samples had been synthesized using a novel technique designed to suppress the generation of high molar mass by-products. While size exclusion chromatography data indicated that the samples were monodisperse, low molar mass by-products were later revealed by temperature gradient interaction chromatography. Viscoelastic data were obtained at temperatures ranging from 75 degrees C to 25 degrees C, and the samples were found to be thermorheologically simple. Sensitivity and uncertainty analyses revealed that among the model parameters, the value of plateau modulus has the strongest effect on model predictions. As molecular models improve, it will become ever more essential to evaluate them using accurate data on materials whose microstructures have been reliably established. This is especially important for materials that are structurally polydisperse. (C) 2011 The Society of Rheology. [DOI: 10.1122/1.3635384]