The statistically steady distribution of water vapour and its characteristics are studied in the framework of the Ornstein–Uhlenbeck (OU) turbulent dispersion model. Particles are advected by a stochastic velocity field with a finite time correlation, and condense as soon as their moisture content exceeds a local saturation value. We discretize the OU model to a finite number of velocity values, and find simple analytical solutions for the bimodal distribution of water vapour and the non-diffusive moisture flux, which perfectly agree with the corresponding Monte-Carlo simulations. Furthermore, we show that these simple models produce results that approximate well the OU Monte-Carlo simulations, suggesting that they could be used as general tools to understand correlated stochastic processes that involve condensation.