Holistic processing, a hallmark of face processing, can be measured by the composite face effect: adults have difficulty recognising the top half of a face when it is aligned with a new bottom half, unless holistic processing is disrupted by misaligning the two halves. Like the recognition of facial identity, holistic processing is impaired when faces are inverted. To obtain a more refined measure of the influence of orientation on holistic face processing, we administered the composite face task to adults at each of seven orientations. In both experiment 1 (in which orientations were randomly intermixed) and experiment 2 (in which orientations were blocked), the composite face effect decreased linearly with rotation. We conclude that holistic processing is tuned to upright faces, diminishes as faces deviate from upright, and becomes insignificant once faces reach a sideways orientation. We propose a hierarchical model of face perception in which linear decreases in holistic processing underlie qualitative shifts in other aspects of face perception.