We examine current Large Hadron Collider constraints on some simple $Z\prime$ models that significantly improve on Standard Model fits to $b\to s\mu +\mu -$ 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 $b\to s\mu +\mu -$ 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 $Z\prime$ boson is less than 300 GeV.