In models with stochastic modification of the Schroedinger equation, the Schroedinger expansion of the wave function is interrupted by repeated spontaneous stochastic localizations, called `quantum jumps`. In the K-model, this stochastic modification of the Schroedinger evolution of the quantum state is based on a modification of the notion of the state itself. After recalling the main features of the model, the decay of superpositions in a cloud chamber is discussed, and a refined version of the model is presented. (R.P.) 8 refs.