The specificity and sensitivity of T-cell recognition is vital to the immune response. Ligand engagement with the T-cell receptor (TCR) results in the activation of a complex sequence of signalling events, both on the cell membrane and intracellularly. Feedback is an integral part of these signalling pathways, yet is often ignored in standard accounts of T-cell signalling. Here we show, using a mathematical model, that these feedback loops can explain the ability of the TCR to discriminate between ligands with high specificity and sensitivity, as well as provide a mechanism for sustained signalling. The model also explains the recent counter-intuitive observation that endogenous 'null' ligands can significantly enhance T-cell signalling. Finally, the model may provide an archetype for receptor switching based on kinase-phosphatase switches, and thus be of interest to the wider signalling community.