We describe experiments on the fall of a single sphere through two different types of Boger fluids. Particular attention is given to the dependence of the equilibrium drag on the sphere on the Weissenberg number and the ratio beta between the radius of the sphere and that of the containing cylinder. Some attention is also given to the transient build up to steady state flow, where it is shown that a significant overshoot in velocity is sometimes observed over an inordinately long timescale. In general terms, the experiments show that the normalized drag can be very high for the limiting cases beta --> 0 and beta --> 1, with much smaller values at some intermediate values of beta. Numerous questions remain and there is at present a significant gulf between available experimental data and reliable numerical simulations for simple viscoelastic models.