It is known that the zero shear viscosity of a polydisperse melt of linear polymers depends only on its weight-average molecular weight, whereas its recoverable compliance increases with polydispersity. These facts can be exploited to design model viscoelastic fluids using mixtures of short and long chains of the same homopolymer (bidisperse mixtures). The composition required to obtain a bidisperse mixture with the desired viscosity can be calculated from the molecular weights of the components, and the known relationship between viscosity and weight-average molecular weight. The terminal viscoelastic properties of such a bidisperse mixture are estimated from theoretical predictions for the compliance of bidisperse mixtures available in the literature. These predictions suggest that the elasticity of bidisperse mixtures can be varied independent of their viscosity by appropriately choosing the molecular weights of their components and their composition. This strategy is applied here on bidisperse mixtures of monodisperse 1,4-polyisoprene, which are shown to display second-order fluid behavior over a reasonable range of accessible shear rates. The same procedure is also applied to mixtures of PDMS polymers which are not particularly monodisperse. Rheological measurements show that the elasticity of these polyisoprene and PDMS mixtures can indeed be varied without changing their viscosity. Such materials are ideally suited to study structure-rheological properties relationships in blends of immiscible viscoelastic fluids.