Abstract Effective field theory-based searches for new physics at colliders are relatively insensitive to interactions involving only right-handed down-type quarks. These interactions can hide amongst jet backgrounds at the LHC, and their indirect effects in electroweak and Higgs processes are small. Identifying scenarios in which these interactions dominate, we can naturally pick out just two tree-level mediators, both scalar diquarks. Over the full parameter space of these states, we analyse exotics searches at current and future hadron colliders, Higgs signal strength constraints, and indirect constraints from flavour physics, finding genuine complementarity between the data sets. In particular, while flavour constraints can exclude diquarks in the hundreds of TeV mass range, these can be evaded once a flavour structure is imposed on the couplings, as we illustrate by embedding the diquarks within a composite Higgs model. In combination, however, we show that flavour and collider constraints exclude down-type diquarks to multi-TeV scales, thus narrowing the remaining hiding places for new interactions amongst LHC data.