When an excess appears in LHC data, we should be comparing the data with entire classes of models, to get an immediate sense of which ones could conceivably be relevant. Often, the new physics is likely to be a relatively narrow s-channel resonance. In this case, a simplified model of the resonance can translate an estimated signal cross section into model-independent bounds on the product of the production and decay branching ratios. This quickly reveals whether a given class of models could possibly produce a signal of the required size at the LHC. This talk will outline a general framework, show how it operates for resonances with different numbers of production and decay modes, and analyzes cases of experimental interest, including resonances decaying to dibosons, diphotons, dileptons, or dijets. If the LHC experiments were to report searches for BSM resonances in the simplified limits variable $\zeta$ defined here, the community could home in more quickly on the models most likely to explain any observed excess.