  Consistent heterotic free fermionic string models are classified in terms of
their number of spacetime supersymmetries, N. For each of the six distinct
choices of gravitino sector, we determine what number of supersymmetries can
survive additional GSO projections. We prove by exhaustive search that only
three of the six can yield N = 1, in addition to the N = 4, 2, or 0 that five
of the six can yield. One choice of gravitino sector can only produce N = 4 or
0. Relatedly, we find that only Z_2, Z_4, and Z_8 twists of the internal
fermions with worldsheet supersymmetry are consistent with N=1 in free
fermionic models. Any other twists obviate N=1.
