  We explore the sensitivity of Tevatron data to heavy new physics effects in
differential dijet production rates using the SMEFT in light of the fact that
consistent and conservative constraints from the LHC cannot cover relatively
low cutoff scales in the EFT. In contrast to the results quoted by the
experimental collaborations and other groups, we find that, once consistency of
the perturbation expansion is enforced and reasonable estimates of theoretical
errors induced by the SMEFT series in $\frac{E}{\Lambda}$ are included, there
is no potential to constrain four-quark contact interactions using Tevatron
data. This shows the general difficulty of constraining physics
model-independently using fairly imprecise measurements, limited by low
luminosity and/or systematic errors inherent to the precision of the detectors.
