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The well-known problem of adaptive signal detection in background interference is addressed for situations where only a small number of training data samples are available. Since all known constant false-alarm rate (CFAR) adaptive detectors such as the traditional generalized likelihood-ratio test (GLRT), adaptive matched filter (AMF), and adaptive coherence estimator (ACE) detectors use the generic maximum-likelihood (ML) sample covariance matrix estimate (CME), the sample support necessary for accurate detection must significantly exceed the adaptive system (e.g., antenna array) dimension M, and so is often impractically large. For scenarios with a limited number m of dominant covariance matrix eigenvalues, more efficient diagonally loaded CMEs are available, whose required sample support is comparable to m (rather than M) for efficient interference mitigation. Since detectors that adopt these and other CMEs that use some a~priori information are not strictly CFAR, here we consider a "two-stage" adaptive detection scheme that optimally partitions the total sample support T into two sets: T_CME data samples are used to design the adaptive filter (beamformer), and the remaining T_CFAR samples are used to calculate the adaptive scalar false-alarm threshold. We present a comparative analysis of the detection performance of "one-stage" CFAR and "two-stage" adaptive detectors.