natural – albeit surprising – explanation by analogy with the properties of single-molecule magnets [@review]. These are metal-organic clusters with large composite spins: some of the most studied include the so called Mn$_{12}$ and Fe$_8$ systems, both of which can be thought of as an ensemble of identical, weakly interacting nanomagnets of net spin S = 10 with an Ising-like anisotropy. The degenerate $M_{\rm s} = \pm S$ states are split by the ligand electric field into a series of doublets. At temperatures smaller than the level separation, the spins flip by resonant tunnelling through a quasi-classical barrier. The signature of a resonant tunnelling effect in Fe$_8$ is a peak in the low temperature relaxation rate around $H = 0$ [@Sa]. It quickly became clear that to understand the resonant tunnelling both dipolar and dynamic nuclear spin contributions to the interactions need to be accounted for. The typical dipolar field in such a system is $\approx 0.5$ K, and the relevant tunnel splitting $\Delta E$ of the order 10$^{-8}$ K, meaning that a broad distribution of dipolar field and a static hyperfine contribution would force all the spins off resonance. Prokof’ev and Stamp [@PS] proposed that dynamic nuclear fluctuations can 