The shallow-water equations are supplemented by a moisture equation in order to model effects of latent heat release on the horizontal propagation of disturbances. Since latent heating in regions of upward motion compensates the reduction in perturbation temperature due to lifting, buoyancy effects are reduced and disturbances propagate more slowly. Analytic solutions are obtained to illustrate this effect, a good example being provided by the collapse of an initial horizontal temperature discontinuity. Another interesting example is provided by the case of disturbances propagating through a region from one side. Moist regions are found to have front and rear boundaries which both move faster than rainbands do inside the moist region. If random disturbances are passed through a region which is initially saturated, the relative humidity drops until it reaches a value which depends on the disturbance level.