T lymphocytes are believed to alter their sensitivity to TCR stimulation by means of a tunable cellular activation threshold. We present two modelling examples which show that the concept of a tunable threshold can be made mechanistically plausible. The tunable threshold is treated as an emergent property of the dynamics of the T cell's signalling machinery. In addition, we discuss how the dynamic properties of activation threshold tuning can be determined experimentally with the aid of these two models. We propose a novel 'avidity selection' mechanism for the initial stages of the immune response, based on the properties of the T cell activation threshold tuning mechanism we propose for the commitment to differentiation. Our main finding is that activation threshold tuning allows T cells to respond to relevant ligands with a detection threshold that is (i) uniform across both the T cell repertoire and the secondary lymphoid tissues, while (ii) retaining tolerance to autostimulation. Our analysis indicates that central tolerance enhances the efficiency of peripheral tolerance, casting new light on the role of negative selection in the thymus.