  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 $\Lambda$ are
within ~ 15% of the latest limits from the LHC experiments.
