Accurate prediction of the settling velocity of a single particle in a quiescent, non-Newtonian fluid is often required for analysis of fluid-particle systems, e.g. the design and operation of slurry pipelines and solid-liquid separation processes. Wilson et al. presented a direct method that was able to provide reasonable predictions of the terminal settling velocity of a sphere in a fluid with a yield stress. This method is somewhat limited in its applicability: if the fluid yield stress is greater than the calculated reference shear stress, the correlation cannot produce a prediction of terminal settling velocity. Measurements of terminal fall velocities of precision spheres in quiescent Kaolinite-water suspensions were collected in the present study. Kaolinite volume concentrations were 10.6-21.7 % (0.106-0.217L/L) resulting in suspension yield stresses of 1.3-30Pa. Both Casson and Bingham models were satisfactory for modelling the clay-water mixture rheology. An analogy of the Wilson-Thomas analysis for the pipe flow of non-Newtonian fluids was used to develop a new method for predicting terminal settling velocity of a sphere in a viscoplastic fluid. The new method does not have the limitations of the Wilson et al. method, and also provides more accurate predictions. The experimental results obtained here show that further research is needed to better characterize particle behaviour at low shear Reynolds numbers (Re*<10).