  We investigate some issues relating to recently proposed fractional
superstring theories with $D_{\rm critical}<10$. Using the factorization
approach of Gepner and Qiu, we systematically rederive the partition functions
of the $K=4,\, 8,$ and $16$ theories and examine their spacetime supersymmetry.
Generalized GSO projection operators for the $K=4$ model are found. Uniqueness
of the twist field, $\phi^{K/4}_{K/4}$, as source of spacetime fermions is
demonstrated. Last, we derive a linear (rather than quadratic) relationship
between the required conformal anomaly and the conformal dimension of the
supercurrent ghost.
