It is demonstrated for the first time that the presence of a small number of fast, nonlocal electrons can dramatically change the thickness of and electric field in the near-wall sheath. Even if the density of the nonlocal fast group, n(f), is much less than the density of the bulk electrons, n(b) (n(f)similar to 10(-5)n(b)), the near-wall potential can increase dramatically resulting in a comparable increase in the sheath thickness. Because of this low fractional density, the average energy (electron temperature T-e) of all electrons is little changed from that of the bulk, yet the near-wall potential drop can increase to tens of T-e/e. More importantly, due to the nonlocal nature of this group of electrons, the near-wall sheath potential is found to be independent of T-e and is determined only by the energy of the fast group.