Constraining four-fermion operators using rare top decays

New physics can manifest itself by an appreciable increase of the decay rate of top quarks in rare flavour-changing final states. Exploiting the large top quark production rate at the LHC, we bound four-fermion operators contributing to non-resonant $t\rightarrow \ell^+\ell^- j$ using different signal regions of the latest LHC searches for $t\rightarrow Zj$. We also provide prospects for the high-luminosity LHC to test these as well as four-fermion operators contributing to $t\rightarrow b\overline{b}j$, based on improved analysis strategies of existing searches. We single out all weakly-coupled ultraviolet completions inducing such contact interactions at tree level and translate the previous bounds to the parameter space of specific complete models. Being above the TeV, LHC bounds from rare top decays improve over those from flavour physics, electroweak precision data and other LHC searches in several cases.