Shell-model calculations for 127,129In and 129,131Sb are presented, and interpreted in the context of the particle-core coupling scheme, wherein proton g9/2 holes or g7/2 particles are added to semimagic 128,130Sn cores. These results indicate that the particle-core coupling scheme is appropriate for the Sb isotopes, whilst less so for the In isotopes. B(E2) excitation strengths are also calculated, and show evidence of enhanced collectivity in both Sb isotopes, especially 131Sb. This observation suggests that 131Sb would be an excellent case for an experimental study seeking to investigate the early onset of collectivity near 132Sn.