Abstract: The dispersive readout scheme enables quantum non-demolition measurement of superconducting qubits. An increased readout power can shorten the readout time and reduce the state discrimination error but can promote qubit transitions into higher noncomputational states. These measurement-induced transitions present a severe obstacle to improving the qubit readout. The physics of the effect has been only studied in the context of transmon qubits thanks to approximations unique to this qubit type. In the talk, I will introduce the problem and review the existing experimental and theoretical results. Building upon the concept of dressed coherent states, I will explain how one can think about these transitions in an arbitrary qubit system with few degrees of freedom. Taking advantage of the presented approach, I will show how to predict the number of microwave photons causing such transitions using a fluxonium qubit as an example system.