Abstract We have made a study of the lowest-lying 7 2 − isobaric analogue resonances in the odd isotopes of antimony by analysis of the elastic scattering of protons from even isotopes of tin. These resonances correspond to low-lying states in odd isotopes of tin. The states of interest are the 2.76 MeV state in 125Sn, the 2.73 MeV state in 123Sn and the 2.59 MeV and 2.69 MeV states in 121Sn. Measurements of cross section and polarization were made for protons scattered from 124Sn, 122Sn and 120Sn at bombarding energies from 9.85 MeV to 10.90 MeV. Theoretical fits to the data were made using resonance terms of the Breit-Wigner form in the collision matrix. The fits to the data established the spins and parities of the resonances. The resonance parameters from these fits were used to calculate spectroscopic factors for the states, using the approaches of Thompson, Adams and Robson, and of Mahaux and Weidenmüller. The optical-model parameters used to describe the non-resonant background scattering were obtained by fitting off-resonance angular distributions. An investigation has shown large sensitivities to various parameters of the optical potential. Cross-section measurements for the decay of the 7 2 − resonances to 2 + and 3 − excited states were made in order to obtain information about the admixtures to the analogue states.