Recent signs of a Standard Model-like Higgs at 125 GeV point towards large A-terms in the MSSM. This presents special challenges for gauge mediation, which by itself predicts vanishing A-terms at the messenger scale. In this paper, we review the general problems that arise when extending gauge mediation to achieve large A-terms, and the mechanisms that exist to overcome them. Using these mechanisms, we construct weakly-coupled models of low-scale gauge mediation with extended Higgs-messenger couplings that generate large A-terms at the messenger scale and viable mu/Bmu-terms. Our models are simple, economical, and complete realizations of supersymmetry at the weak scale.