All gamma cameras used in nuclear medicine have finite energy resolution, thereby making discrimination of scattered radiation from photopeak events extremely difficult. Different scatter-correction methods have been developed to prevent scattered radiation from degrading the image quality of a gamma-ray image. Rejecting scatter events on an event-by-event basis in data acquisition as much as possible is a preferable option. However, the fact that all scattered events cannot be rejected without sacrificing primary photon sensitivity might require applying scatter correction after acquisition; nevertheless, the scattered photons should not be allowed to enter into the image. Most conventional approaches reject scatter events by using energy windows (EWs). Milster et al. introduced the likelihood window (LW) as an alternative. We also employed this method in a modular gamma scintillation camera that has a 2 x 2 array of photomultipliers (PMTs) coupled to a NaI(TI) crystal. In this work, another scatter rejection scheme, the Bayesian window (BW), is developed. In contrast to the LW and the EW, the BW takes into account the simulated or actual scatter spectrum in making a decision to accept or reject a particular photon. This work compares the effectiveness of scatter rejection by BW, LW, and EW through receiver operating characteristic (ROC) studies. Results indicate that the BW method is the preferable choice.