Edge-illumination x-ray phase-contrast tomography (EIXPCT) is a promising imaging technology where partially opaque masks are utilized with laboratory-based x-ray sources to estimate the distribution of the complex-valued refractive index. EIXPCT resolution is mainly determined by the period of a sample mask, but can be significantly improved by a dithering technique. Here, dithering means that multiple images per tomographic view angle are acquired as the object is moved over sub-pixel distances. Drawbacks of dithering include increased data-acquisition times and radiation doses. Motivated by the flexibility in data-acquisition designs enabled by a recently developed joint reconstruction method, a novel partial-dithering strategy for EIXPCT data-acquisition is proposed. In this strategy, dithering is implemented at only a subset of the tomographic view angles. The strategy can result in spatial resolution comparable to that of the conventional full-dithering strategy, where dithering is performed at every view angle, but the acquisition time is substantially decreased. Here, the effect of dithering parameters on image resolution is explored.