The authors used a state-trace methodology to investigate the informational dimensions used to recognize old and conjunction faces (made by combining parts of separately studied faces). Participants in 3 experiments saw faces presented for 1 s each. They then received a recognition test; faces were presented for varying brief durations and participants made 3 responses: old/new judgments, confidence judgments, and an indication of whether each response was based on memory for a feature or in general familiarity. Experiments 1 and 3 showed that, given equal confidence, familiarity-based responses were more accurate than feature-based responses; these results provide strong support for a multidimensional model in which 2 separate types of information contribute to confidence and accuracy responses. Experiment 2 showed that this feature/familiarity difference disappeared when conjunction faces were included in the test, supporting a unidimensional model in which confidence and accuracy are based on a single type of information. Inclusion of conjunction faces fundamentally alters the way that previously encountered faces are processed; participants apparently rely entirely on feature-based information to recognize them.