The effective radial deposition profile of deuterium pellets injected into the Joint European Torus (JET) and Tokamak Fusion Test Reactor (TFTR) tokamaks has been determined from Thomson scattering diagnostic measurements of electron density taken immediately after pellet injection. The pellet ablation rate deduced from these measurements differs from that predicted by conventional pellet ablation theory. The possibility of enhanced radial transport during the ablation process has been examined to determine whether this can explain the difference between theory and experiment, but no evidence has been found to support such an explanation. The temporal evolution of the Balmer-alpha light emitted during pellet ablation is found to be different from the effective pellet ablation rate determined from the density profile measurements. We conclude that the shielding mechanisms of conventional pellet ablation models need modifications to predict and reproduce the observed effective ablation rate and penetration depth.