  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 model-independent bounds on the product of the branching ratios
corresponding to production and decay. 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 $\zeta$ 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.
