The precedence effect is a phenomenon that may occur when a sound from one direction (the lead) is followed within a few milliseconds by the same or a similar sound from another direction (the lag, or the echo). Typically, the lag sound is not heard as a separate event, and changes in the lag sound’s direction cannot be discriminated. The hypothesis is proposed in this study that these two aspects of precedence (echo suppression and discrimination suppression) are at least partially independent phenomena. Two experiments were conducted in which pairs of noise bursts were presented to subjects from two loudspeakers in the horizontal plane to simulate a lead sound and a lag sound (the echo). Echo suppression threshold was measured as the minimum echo delay at which subjects reported hearing two sounds rather than one sound; discrimination suppression threshold was measured as the minimum echo delay at which subjects could reliably discriminate between two positions of the echo. In Experiment 1, it was found that echo suppression threshold was the same as discrimination suppression threshold when measured with a single burst pair (average 5.4 msec). However, when measured after presentation of a train of burst pairs (a condition that may produce “buildup of suppression”), discrimination suppression threshold increased to 10.4 msec, while echo suppression threshold increased to 26.4 msec. The greater buildup of echo suppression than of discrimination suppression indicates that the two phenomena are distinct under buildup conditions and may be the reflection of different underlying mechanisms. Experiment 2 investigated the effect of the directional properties of the lead and lag sounds on discrimination suppression and echo suppression. There was no consistent effect of the spatial separation between lead and lag sources on discrimination suppression or echo suppression, nor was there any consistent difference between the two types of thresholds (overall average threshold was 5.9 msec). The negative result in Experiment 2 may have been due to the measurements being obtained only for single-stimulus conditions and not for buildup conditions that may involve more central processing by the auditory system.