We have studied layer-by-layer polyelectrolyte self-assembly on pristine individual single-wall carbon nanotubes as a function of solution ionic strength. We report the existence of an ionic strength threshold for the deposition, below which the majority of nanotubes remain uncoated. Once the ionic strength reaches the threshold value, the majority of the individual nanotubes become coated with polyelectrolytes. Our results indicate that the self-assembly process likely involves wrapping of polymer chains around nanotubes and that the polymer chain's ability to bend in order to accommodate the nanotube curvature is one of the critical parameters controlling layer-by-layer electrostatic self-assembly on these one-dimensional templates.