The channelized radiometer is a well-known intercept receiver. We analyze its performance when different constant false alarm rate (CFAR) strategies are used to set a detection threshold based on values of some reference cells. The studied conventional methods are cell-averaging (CA) and order statistics. The proposed iterative methods for setting the detection threshold are forward consecutive mean excision (FCME) with the CA scaling factors in (final) detection decision (FCME+CA), backward consecutive mean excision (BCME) with the CA scaling factors in detection (BCME+CA) and a method that uses the CA scaling factors in both censoring and detection (CA+CA). The results show that iterative CFAR methods can improve detection performance compared to the baseline methods.