Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. In two recent papers [1,2] we have shown that the leading mechanism responsible for the enhancement of energy relaxation times of weakly anharmonic qubits is the presence of number non-conserving terms in the Josephson potential, which activate additional multi-photon and qubit-cavity correlated relaxation channels in the presence of drives. We address here a realistic experimental setup and account for the joint effects of radiative (Purcell) decay at finite temperature and dephasing.  Moein Malekakhlagh, Alexandru Petrescu, Hakan E. Tureci, Lifetime renormalization of weakly anharmonic superconducting qubits: I. Role of number non-conserving terms, arXiv:1809.04667  Alexandru Petrescu, Moein Malekakhlagh, Hakan E. Tureci, Lifetime renormalization of driven weakly anharmonic superconducting qubits: II. The readout problem, arXiv:1908.01240 *This work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Award No. DE-SC0016011.