Receiver operating characteristic (ROC) curves and psychometric functions for detection of 1000‐Hz sinusoids presented against a background of narrow‐band noise were obtained using a one‐interval rating‐scale procedure. Signals were added to noise alone (simpledetection) or to noise plus sinusoidal pedestal (pedestaldetection). While almost all stimulus‐oriented theories of signal detectability predict a monotonically decreasing relation for the slope of the ROC curve as a function of signal strength, slopes of the empirically determined ROC's never showed a systematic decrease with increases in signal amplitude. Significant differences between the range of the psychometric functions for simple‐ and pedestal‐detection conditions were noted. Two modifications of the basic signal‐detection approach, a fluctuating criterion model and a neural counting scheme, are proposed to account for the data. An investigation of the neural counting model was carried out in computer simulation, and the influence of various exponents in the power‐law transducer function relating stimulus energy and neural counts was examined. Implications of the theoretical and empirical results for our notions about the nature of the underlying probability distributions and decision mechanisms are discussed.