The highest estimates of the prevalence of commercial contract cheating in Australia come from self-report surveys, which suggest that around 2% of students engage in commercial contract cheating during their higher education studies. However, self-report surveys are limited in that participants under-report socially-undesirable behaviours. In this study, we used an incentivised truth-telling method and surveyed 4098 students from six universities and six independent higher education providers in Australia. We found that 2.46 times more students admitted to commercial contract cheating, via submitting ghost-written assessments, when truth-telling was incentivised (via a Bayesian Truth Serum methodology) rather than when normal self-report survey instructions were used. Using prevalence estimation formulae that are combined with the incentivised truth-telling method, we estimate that 7.9% of students buy and submit assignments from commercial contract cheating services. Additionally, 11.4% outsource assessments via obtaining pre-written work from commercial file-sharing sites. These are substantially higher percentages of commercial contract cheating than self-reports suggest. Furthermore, having a first language other than English was the strongest demographic predictor of Australian students' engagement in commercial contract cheating. We conclude that commercial contract cheating is a more common problem than suggested by self-report surveys. We argue that academic integrity researchers should consider methods beyond standard self-reports to estimate the prevalence of academic misconduct and that efforts to curb commercial contract cheating must be increased.