The thermodynamic miscibility of polyisobutylene (Pm) with butyl rubber (IIR), a copolymer of isobutene and a few mole % isoprene, was established through observation of spontaneous interdiffusion of the polymers Networks were prepared from their blend, in which only the IIR component was cross-linked (NB cannot be cross-linked by sulfur vulcanization or any other method). The blends were significantly stronger (almost 3-fold higher tensile strength) and tougher than neat IIR networks, when compared at equal modulus. This improvement was greater for blends having higher molecular weight PIB. The results show that miscible blends with components having large disparities in their degree of cross linking (infinite in the present case) circumvent the trade-off between stiffness and strength found for conventional elastomers. The operative mechanism is alleviation of local overstresses by configurational rearrangement of unattached, but entangled, chains. This mechanism is common to other approaches that improve the mechanical properties of networks, such as bimodal networks and hydrogel blends.