Listeners perceptually fuse the direct wave from a sound source with its reflections off nearby surfaces into a single sound image, located at or near the sound source (the precedence effect). This study investigated how a brief gap presented in the middle of either a direct wave or simulated reflection is incorporated into the fused image. For short (<9.5 ms) delays between the direct (leading) and reflected (lagging) waves, no sound was perceived from the direction of the lagging wave. For delays between 10 and 15 ms, both sounds were perceived, but the gap was heard only on the leading side. When the gap was only in the correlated lagging sound at short delays, it also was perceived as occurring on the leading side. Moreover, gap detection thresholds were the same for gaps in the leading and lagging sounds, suggesting that the perception of the gap was not suppressed, but rather incorporated into the leading sound. Finally, scalp event-related potentials were not associated with the precedence effect until the gap occurred. This suggests that cortical mechanisms are engaged to maintain fusion when attributes in direct or reflected waves change.