Previously observed positive and negative parity states of 127I have been interpreted using a particle–rotor model. Experimental energies and transition properties have been compared to those predicted by the calculation. The results show that this simple model with very few parameters can successfully explain most of the structure of 127I at low and medium energies. 127I being only three protons beyond the closed Z=50 shell with N=74 relatively far from the middle of the 50–82 neutron region (N=66), there is evidence that it is slightly deformed. The rotational structure of the ΔJ=1 band built on an unusually low-lying g9/2 proton–hole state (9/2+[404]) has been naturally very well predicted as well as other rotational features for the g7/2, d5/2 and h11/2 orbitals. Complete particle–core multiplets have been successfully identified for the first time.