Typical searches for supersymmetry cannot test models in which the two lightest particles have a small ("compressed") mass splitting, due to the small momentum of the particles produced in the decay of the second-to-lightest particle. However, data sets with large missing transverse momentum (ETmiss) can generically search for invisible particle production and therefore provide constraints on such models. We apply data from the ATLAS monojet (jet+ETmiss) and vector-boson-fusion (forward jets and ETmiss) searches to such models. In all cases, experimental limits are at least five times weaker than theoretical predictions.