When can a DNA profile be regarded as unique?

The probability that a defendant's DNA profile is unique in a population of untyped individuals is shown to be bounded below by one minus twice the sum of the match probabilities over the population. This bound assumes that the possibility of laboratory or handling error can be neglected, and applies only when there is no non-DNA evidence in favour of the defendant. There cannot be a completely general lower bound: if there is overwhelming non-DNA evidence that the defendant is not the source of the crime stain, then that is also overwhelming evidence of non-uniqueness. Application to k-locus short tandem repeat (STR) profiles is discussed, and illustrated with calculations based on the 6-STR-locus system used in current UK casework. However, because of the problem of the non-DNA evidence, there seems to be no satisfactory way for an expert witness to address the question of uniqueness in court.