We describe a treatment of the absorption of solar neutrinos by 127I, in connection with a proposed solar neutrino detector. With an in-medium value of −1.0 for the axial-vector coupling constant g A , we obtain a 8B-neutrino cross section of 3.3×10 −42 cm 2, and a 7Be cross section that is uncertain but large enough so that with the standard-solar-model fluxes the 7Be neutrinos would contribute approximately as much as the 8B neutrinos. We then apply the improved techniques to energies relevant to the neutrinos from muon decay at rest that obtain at the LAMPF beam dump, where an experiment is underway to finalize a calibration of the 127I. We find that forbidden operators, which play no role in solar-neutrino absorption, contribute nonnegligibly to the LAMPF cross section, and that the preliminary LAMPF mean value is significantly larger than our prediction.