Abstract: We examine current Large Hadron Collider constraints on some simple Z′ models that significantly improve on Standard Model fits to b→sμ+μ- transition data. The models that we consider are the ‘third family baryon number minus second family lepton number’ (B3-L2) model and the ‘third family hypercharge’ model and variants. The constraints are applied on parameter regions of each model that fit the b→sμ+μ- transition data and come from high-mass Drell–Yan di-muons and measurements of Standard Model processes. This latter set of observables place particularly strong bounds upon the parameter space of the B3-L2 model when the mass of the Z′ boson is less than 300 GeV.