We analyze a class of generalized two-ray (GTR) fading channels that consist of two line-of-sight (LOS) components with random phase plus a diffuse component. We derive a closed-form expression for the moment-generating function of the signal-to-noise ratio (SNR) for this model, which greatly simplifies its analysis. This expression arises from the observation that the GTR fading model can be expressed in terms of a conditional underlying Rician distribution. We illustrate the approach to derive simple expressions for statistics and performance metrics of interest, such as the amount of fading, the level crossing rate, the symbol error rate, and the ergodic capacity in GTR fading channels. We also show that the effect of considering a more general distribution for the phase difference between the LOS components has an impact on the average SNR.