Witnesses may construct a composite face of a perpetrator using a computerised interface. Police practitioners guide witnesses through this unusual process, the goal being to produce an identifiable image. However, any changes a perpetrator makes to their external facial-features may interfere with this process. In Experiment 1, participants constructed a composite using a holistic interface one day after target encoding. Target faces were unaltered, or had altered external-features: (i) changed hair, (ii) external-features removed or (iii) naturally-concealed external-features (hair, ears, face-shape occluded by a hooded top). These manipulations produced composites with more error-prone internal-features: participants’ familiar with a target’s unaltered appearance less often provided a correct name. Experiment 2 applied external-feature alterations to composites of unaltered targets; although whole-face composites contained less error-prone internal-features, identification was impaired. Experiment 3 replicated negative effects of changing target hair on construction and tested a practical solution: selectively concealing hair and eyes improved identification.