Ion-conductive membranes used in energy devices are always under compression to minimize a device's contact resistance. In this paper, the conductivity and nanostructure of Nafion membrane, a commonly used ionomer in many electrochemical energy applications, are investigated under compression. Hydrophilic-domain spacing as a function pressure is determined both in the plane (face-on imaging) and thickness (edge-on imaging) directions using small-angle X-ray scattering (SAXS). SAXS results suggest a similar nanostructure in all directions indicating lack of a strong anisotropy when not under compression. However, compressing the membrane induces structural anisotropy where domain spacing gets smaller in the compression (thickness) direction while it elongates in the plane of the membrane. From the domain spacing and water content under compression, the change in conductivity is calculated as a function of pressure and compared with measured data. The findings of this work provide insight into the effect of compression on the three-dimensional morphology of a PFSA membrane and its conductivity, issues that have not been previously explored and are critical to the understanding of ion-conductive membranes.