Dynamical simulations of bulk sedimentation have been carried out, using up to 32 000 solid particles. There is no evidence that the long-range hydrodynamic interactions are screened by changes in the pair correlation function at large distances. Instead the velocity fluctuations and diffusion coefficients diverge linearly with the width of the container, consistent with the random long-range microstructures observed in the simulations. Our data suggest that other mechanisms must be uncovered to account for experimental observations. ©1997 American Institute of Physics.