We discuss how to consistently use Effective Field Theories (EFTs) to set universal bounds on heavy-mediator Dark Matter at colliders, without prejudice on the model underlying a given effective interaction. We illustrate the method for a Majorana fe
rmion, universally coupled to the Standard Model quarks via a dimension-6 axial-axial four-fermion operator. We recast the ATLAS mono-jet analysis and show that a considerable fraction of the parameter space, seemingly excluded by a naive EFT interpretation, is actually still unexplored. Consistently set EFT limits can be reinterpreted in any specific underlying model. We provide two explicit examples for the chosen operator and compare the reach of our model-independent method with that obtainable by dedicated analyses.
