Multiple-scattering approximations to Faddeev calculations of the K − d scattering length are reviewed and compared with publishedKN N − πY N fully reactive Faddeev calculations. A new multiple-scattering approximation which goes beyond the 'fixed-center' assumption for the nucleons is proposed, aiming at accuracies of 5 − 10%. A precise value of the K − d scattering length from the measurement of the K − d 1s atomic level shift and width, planned by the DEAR/SIDDHARTA collaboration, plus a precise value for the K − p scattering length by improving the K − p atom measurements, are essential for extracting the K − n scattering length, for resolving persistent puzzles in low-energyKN phenomenology and for extrapolating intoK-nuclear systems.