Calculations of the neoclassical transport rates due to particles trapped in the helical ripples of a stellarator's magnetic field are carried out, based on solutions of the bounce-averaged kinetic equation. These calculations employ a model for the magnetic field strength, B, which is an accurate approximation to the actual B for a wide variety of stellarator-type devices, among which are Helical-Axis Advanced Stellarators (Helias) as well as conventional stellarators and torsatrons. Comparisons are carried out in which it is shown that the Helias concept leads to significant reductions in neoclassical transport rates throughout the entire long-mean-free-path regime, with the reduction being particularly dramatic in the nu -1 regime. These findings are confirmed by numerical simulations. Further, it is shown that the behaviour of deeply trapped particles in Helias can be fundamentally different from that in classical stellarator/torsatrons; as a consequence, the beneficial effects of a radial electric field on the transport make themselves felt at a lower collision frequency than is usual.