Conventional cell averaging (CA), greater of (GO) and smaller of (SO) constant false alarm rate (CFAR) detectors are considered when an interfering target is present in the reference noise cells. Threshold compensation techniques used previously to improve the performance of a CA detector have been modified and generalised to include GO and SO detectors. It is shown that, using these methods, good relative improvements are obtained for the GO and CA detectors, especially for a small number of reference noise cells. Only slight relative improvements are obtained for the SO detector, however.