  We examine current Large Hadron Collider constraints on some simple $Z'$
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' $(B_3-L_2)$ 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 $B_3-L_2$ model when the mass of the $Z'$ boson is
less than 300 GeV.
