In the earliest stages of evaluating new collider data, especially if a small excess may be present, it would be useful to have a method for comparing the data with entire classes of models, to get an immediate sense of which classes could conceivably be relevant. In this paper, we propose a method that applies when the new physics invoked to explain the excess corresponds to the production and decay of a single, relatively narrow, s-channel resonance. A simplifed model of the resonance allows us to convert an estimated signal cross section into general bounds on the product of the branching ratios corresponding to the dominant production and decay modes. This quickly reveals whether a given class of models could possibly produce a signal of the required size at the LHC. Our work sets up a general framework, outlines how it operates for resonances with different numbers of production and decay modes, and analyzes cases of current experimental interest, including resonances decaying to dibosons, diphotons, dileptons, or dijets. If the LHC experiments were to report their searches for new resonances beyond the standard model in the simplified limits variable ζ defined in this paper, that would make it far easier to avoid blind alleys and home in on the most likely candidate models to explain any observed excesses.