The traditional and more recent methods for computing the inventory dynamics of fusion-fission systems are compared, and the simple relationship between them is demonstrated. It is shown that the traditional approach leads to an expression for the compound doubling time, while the newer approach leads to an expression for the simple doubling time. The fuel stockpile concept is employed to derive expressions for the fuel trajectories of batch-fueled hybrids and clients, and the relationships derived for the batch-fueled systems are applied to a recently proposed conceptual design.