A recent analytical model describing the post-buckling behaviour of an I-section strut experiencing strong axis global–local buckling interaction is extended to investigate the effects of modifying the strut geometry. Using a combination of analytical and finite element (FE) methods, the global slenderness is varied parametrically to determine the regions of interactive behaviour. The effects of stress relieved initial global imperfections are also investigated. It is observed that the strut can exhibit one of five distinctive post-buckling behaviours, the geometries for which are identified. The strut can exhibit local buckling only, global buckling only, global–local buckling interaction with either the global or the local buckling mode being triggered first, or the critical case where both global and local buckling modes are triggered simultaneously. The strut is found to be highly sensitive to initial imperfections in the interactive region, and the implications that this has on the design and the practical use of such components are discussed.