The design of fuel cells and lithium ion batteries is constrained, in part, by mechanical creep and perforation of the polymer electrolyte, a process that is poorly understood at the molecular level. The mechanical stiffness (quantified as shear viscosity) and structure of a widely used polymer electrolyte, Nafion, are studied in the limit of a low solvent volume fraction (=26% v/v H2O) using molecular dynamics simulations. The viscosity is shown to increase by up to 4 orders of magnitude in response to changes in composition representing as little as 2 wt % of system. Two types of compositional changes are considered, changes in solvent volume fraction and counterion type. A system with a counterion X(v+) for every v Nafion monomers and y water molecules is denoted as (RSO3)vX(.)(H2O)y. The following trend is observed in viscosity: (RSO3)(2)Ca > RSO3Na > RSO3H.(H(2)O())3 > RSO3H approximate to RSO3H(.)(H2O)(10). This trend correlates with changes in the strength of the SO3-/Xv+/SO3- cross-links and the size of the cross-link networks. Counterion type is shown to strongly influence the morphology. The simulations are able to reproduce some important experimental trends without crystalline domains or high-MW effects like entanglements, providing a simplified understanding of the mechanical properties of Nafion.