Left panel. Detection completeness as a function of the injected signal using a fully Keplerian search versus a circular orbit search. Red and blue lines are for an injected eccentricity of 0.8, and the brown and purple ones are for injected signals with eccentricity of 0.4. Black horizontal lines on the left show the fraction of false-positive detections satisfying the FAP threshold of 1% using both methods (Keplerian versus circular). While the completeness is slightly enhanced in the low K regime, the fraction of false positives is unacceptable and, therefore, the implicit assumptions of the method (e.g., uniform prior for e) are not correct. Right panel. Distribution of semi-amplitudes K for these false positive detections. Given that the injected noise level is 1.4 m s^-1 (1 m s^-1 nominal uncertainty, 1 m s^-1 jitter), it is clear that signals detected with fully Keplerian log-L periodograms with K below the noise level cannot be trusted.