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We employ density functional theory based phonon transport methods to provide a rigorous understanding of the nature of thermal transport in coherent short -period AlN/GaN superlattices (SLs), with period lengths up to three unit cells of each, and compare these with properties of their bulk constituents. Increasing the period length leads to phonon band folding with frequency gaps and thus smaller phonon velocities and more phonon scattering than in bulk, both of which reduce lattice thermal conductivity (K). Contrary to expectations, we find that velocity variations among larger-period AlN/GaN SLs play only a minor role in cross-plane K reductions, while variations in intrinsic phonon scattering are strongly correlated with their transport behaviors. This work provides insights into the microscopic behaviors of technologically relevant nanostructured materials, which are likely applicable to a wider range of SL systems and other nanostructures.