An important conclusion of earlier work using the ballooning representation is that shear damping of plasma drift waves may be suppressed in a torus. This application of the formalism requires that the diamagnetic frequency have a maximum and implies that drift modes can exist only at this maximum. Here we show that there is a far more general class of torodial drift modes. Shear damping is less well suppressed in these new modes, but they extend over a much larger fraction of the plasma radius. They may therefore have significant implications for plasma transport.