Scanning tunneling microscopy studies show that coarsening of arrays of rectangular single-layer Ag islands on Ag(110) at 220 K and below occurs by one-dimensional (1D) decay of narrower islands, which maintain roughly constant width in the 〈001〉 direction. Adatoms mainly detach from the island ends with 〈001〉 step edges. 1D decay derives from the absence of corner rounding diffusion from 〈001〉 to 〈1̅ 10〉 edges and from inhibited nucleation of new layers on 〈1̅ 10〉 edges. In contrast, rounding from 〈1̅ 10〉 to 〈001〉 edges is active. The island decay rate exhibits an unexpectedly low effective Arrhenius energy due to a combination of strong anisotropy in terrace diffusion and a decrease with temperature of typical island end-to-end separations. Behavior is described by atomistic modeling, which accurately captures both the thermodynamics and the edge diffusion kinetics of the system, in contrast to previous treatments. Kinetic Monte Carlo (KMC) simulations assess model behavior and clarify the driving force for coarsening, as well as various detailed features of the 1D decay process. Refined “atom-tracking” KMC simulations for island configurations matching the experiment recover the experimentally observed island decay times and further elucidate spatial aspects of the transfer of adatoms between islands.