Faces are considered a special class of holistically-processed object. The composite face task is a widely-used tool to infer holistic processing. In this task, recognition of 1 half of a composite face is shown to be hampered by interference from the other half of the face. Although this effect has been documented numerous times, when used in different paradigms, composite faces do not always exhibit effects consistent with holistic processing. The present study explored the cause of these discrepant findings by combining a composite face task with a signal-to-respond paradigm. The amount of time to make a face recognition decision was manipulated by introducing a response signal, and the resulting changes in accuracy were mapped over the time course of processing, which was then used to fit a speed-accuracy trade-off model. We found that holistic processing emerges late in the time course after approximately 400 ms processing time for easy-to-discriminate faces and after approximately 1000 ms for difficult-to-discriminate faces. (PsycInfo Database Record (c) 2021 APA, all rights reserved).