  In the spirit of a previous study of the tetrahedral group $T \simeq A_4$, we
discuss a minimalist scheme to derive the neutrino mixing matrix using the
double tetrahedral group $T'$, the double cover of $T$. The new features are
three distinct 2-dimensional representations and complex Clebsch-Gordan
coefficients, which can result in a geometric source of CP violation in the
neutrino mass matrix. In an appendix, we derive explicitly the relevant group
theory for the tetrahedral group $T$ and its double cover $T'$.
