This paper reviews studies carried out by the author and colleagues in which a brain wave measure, the contingent negative variation (CNV), was explored using different paradigms as a measure of deviant sexual desire in child sex offenders and of criminal (especially violent) recidivism in mentally disordered offenders. CNV was recorded using: (1) a Go/No Go paradigm in a sample of mentally disordered offenders admitted to Special Hospital in the UK and subsequently followed up over a number of years; and (2) a match/mismatch paradigm in a sample of child sex offenders admittted to a sex offender treatment unit in NZ. A CNV correlate of impulsivity, recorded using a Go/No Go paradigm, has been found to be potentially useful for predicting recidivism in mentally disordered offenders. An hypothetical CNV correlate of sexual desire, recorded using a match/mismatch paradigm, has been found to be potentially useful for identifying paedophiliac individuals. While the combined use of these measures offers a potential means of identifying child sex offenders who are likely to recidivate, their use raises some important ethical issues, which are briefly discussed.