A two-stage four-level conditional detector is described. The detector is a constant-false-alarm-rate detector. Its performance is compared with that of a single-stage (fixed-sample-size) four-level conditional detector. In a finite-sample comparison the noise is assumed to have a Rician probability density function, which is the probability density function of the output of an envelope detector in a radar receiver when the background noise is white Gaussian noise. In an asymptotic comparison the asymptotic relative efficiency (ARE) is defined and expressions are given for calculating the ARE. Both finite and asymptotic results show significant reduction in the average sample size in the no-signal case. Therefore the proposed two-stage detector is suitable for signal detection in a situation where the no-signal hypothesis has a higha prioriprobability.