As 'Ulysses' moved to latitudes above 45¿, the regular, recurring series of mid-latitude high-speed streams is no longer observed out to 4 AU. However, the associated, near-relativistic particle modulation persists to at least 70¿. We explain this remote shadowing as due to the spread in latitude of the fast streams beyond the 'Ulysses' trajectory and show that an estimate of the particle diffusion coefficient within the stream, based on magnetometer data, yields sufficient modulation to make the model plausible. ¿ American Geophysical Union 1995