We give further consideration to the fall of a sphere through highly elastic liquids. Earlier work is extended to include the case of a tightly-fitting cylindrical container (beta approximate to 0.9). For all three elastic liquids investigated (two Boger fluids and the International Test Fluid S1), there is a decrease in drag as the Weissenberg number W-e increases. In the case of the Boger fluids, the drag reduction is the order of 17% before plateauing out, with virtually constant values of the normalized drag for a range of Weissenberg numbers. Owing to the obvious and unavoidable limit on the weight of the sphere, it was not possible to search for the anticipated drag enhancement due to extensional viscosity effects at high W-e. To overcome this frustration, we considered the related problem of pressure-driven flow past a lone stationary sphere in a tightly fitting cylindrical container. In this case it was possible to observe the full range of phenomena, i.e, a Newtonian plateau response at very small W-e, followed by a drag decrease to a second plateau region and then a significant drag enhancement at high W-e.