  We study the inclusion of $\mathcal O(1/\Lambda^4)$ effects in the Standard
Model Effective Field Theory in fits to the current Drell-Yan data at the LHC.
Our analysis includes the full set of dimension-6 and dimension-8 operators
contributing to the dilepton process, and is performed to next-to-leading-order
in the QCD coupling constant at both $\mathcal O(1/\Lambda^2)$ and $\mathcal
O(1/\Lambda^4)$. We find that the inclusion of dimension-6 squared terms and
certain dimension-8 operators has significant effects on fits to the current
data. Neglecting them leads to bounds on dimension-6 operators off by large
factors. We find that dimension-8 four-fermion operators can already be probed
to the several-TeV level by LHC results, and that their inclusion significantly
changes the limits found for dimension-6 operators. We discuss which
dimension-8 operators should be included in fits to the LHC data. Only a
manageable subset of two-derivative dimension-8 four-fermion operators need to
be included at this stage given current LHC uncertainties.
