The first-order statistics of the vecter sum of a complex Gaussian variable and N complex exponentials with constant amplitudes but random independent phases are used to model a non-Rayleigh fading signal. Envelope detection, optimal for detecting Rayleigh (N = 0) and Rician (N = 1) signals, is also shown to be optimal for the considered non-Rayleigh signals in additive white Gaussian noise. However, the signal-to-noise ratio required to detect the latter signal for N = 2 may be substantially higher than for the former cases. Possible applications of this fading model to studies of multipath fading, non-Rayleigh sea echoes, microwave or laser radar detection and tracking are discussed.