Decoherence and disentanglement are phenomena central to quantum mechanics. Here, we consider the relative rates of decoherence and disentanglement in two-qubit, three-qubit, and two-qutrit systems when subject to pure dephasing noise alone, and a very recent result for d x d systems. Of particular interest is the specific counterintuitive effect related to the nonadditivity of such weak noises, known as Entanglement Sudden Death (ESD), in which the entanglement of a composite quantum system goes abruptly to zero in finite time, coherence only exponentially decaying. We discuss these results in the context of the foundations of quantum mechanics.