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It is shown that isospin-breaking corrections to the pion-deuteron scattering length can be very large, because of the vanishing of the isospin-symmetric contribution to this scattering length at leading order in chiral perturbation theory. We further demonstrate that these corrections can explain the bulk of the discrepancy between the recent experimental data on pionic hydrogen and picnic deuterium. We also give the first determination of the electromagnetic low-energy constant f(1). (c) 2006 Elsevier B.V. All rights reserved.