The problem of adaptive detection in the situation of signal mismatch is considered; that is, the actual signal steering vector is not aligned with the nominal one. Two novel tunable detectors are proposed. They can control the degree to which the mismatched signals are rejected. Remarkably, it is found that they both cover existing famous detectors as their special cases. More importantly, they possess the constant false alarm rate(CFAR)property and achieve enhanced mismatched signal rejection or improved robustness than their natural competitors. Besides, they can provide slightly better matched signals detection performance than the existing detectors. The problem of adaptive detection in the situation of signal mismatch is considered; that is, the actual signal steering vector is not aligned with the nominal one. They can control the degree to which the mismatched signals are rejected. Remarkably, it is found that they both cover existing famous detectors as their special cases. More importantly, they possess the constant false alarm rate (CFAR) property and achieve enhanced mismatched signal rejection or improved robustness than their natural competitors. slightly better matched signals detection performance than the existing detectors.