A broad class of scenarios for new physics involving additional strongly-interacting fields predict signatures at hadron colliders which consist solely of large numbers of jets and substantial missing transverse energy. We investigate the prospects for discovery in such scenarios using a search strategy in which jet multiplicity and missing transverse energy are employed as the primary criteria for distinguishing signal from background. We examine the discovery reach this strategy affords in an example theory (a simplified supersymmetric model whose low-energy spectrum consists of a gluino, a light stop, and a light neutralino) and demonstrate that it frequently exceeds the reach obtained via other, alternative strategies.