T cell activation is a crucial checkpoint in adaptive immunity, and this activation depends on the binding parameters that govern the interactions between T cell receptors (TCRs) and peptide-MHC complexes (pMHC complexes). Despite extensive experimental studies, the relationship between the TCR-pMHC binding parameters and T cell activation remains controversial. To make sense of conflicting experimental data, a variety of verbal and mathematical models have been proposed. However, it is currently unclear which model or models are consistent or inconsistent with experimental data. A key problem is that a direct comparison between the models has not been carried out, in part because they have been formulated in different frameworks. For this Analysis article, we reformulated published models of T cell activation into phenotypic models, which allowed us to directly compare them. We find that a kinetic proofreading model that is modified to include limited signalling is consistent with the majority of published data. This model makes the intriguing prediction that the stimulation hierarchy of two different pMHC complexes (or two different TCRs that are specific for the same pMHC complex) may reverse at different pMHC concentrations.