The paper focuses on a recently proposed coherent model for non-Gaussian clutter, which achieves a log-normal amplitude and a nearly uniform phase by means of a nonlinear (exponential) transformation of a complex Gaussian process with suitable correlation properties. Along with the relevant features, few drawbacks of the model are put forth, concerning the lack of symmetry and the nonstationarity of the associated bandpass process. A simple modification of the model, namely the addition of a uniform phase, is suggested which restores stationarity and symmetry while preserving its remaining features.