The hierarchy of scales which would allow dimension-six contact interactions to parametrise New Physics may not be verified at colliders. Instead, we explore the feasability and usefulness of parametrising the high-energy tail of distributions at the LHC using form factors. We focus on the process pp -> l+l- in the presence of t (or s)-channel New Physics, guess a form factor from the partonic cross-section, and attempt to use data to constrain its coefficients, and the coefficients to constrain models. We find that our choice of form factor decribes t-channel exchange better than a contact interaction, and the coefficients in a particular model can be obtained from the partonic cross-section. We estimate bounds on the coefficients by fitting the form factors to available data. For the parametrisation corresponding to the contact interaction approximation, our expected bounds on the scale $Λ$ are within ~ 15% of the latest limits from the LHC experiments.

5 pages, 4 figures