This research project examines the determinants of tax non-compliance when there is a "tax advice" industry supplying schemes which help taxpayers reduce their tax liability. Our approach is to apply a traditional industrial organisation framework to model the behaviour of this industry. This suggests that the level of non-compliance is affected by the distribution of pretax income, the progressivity of the tax-schedule and the way in which monitoring and penalties vary with income. We show that lower pre-tax income inequality, as well as a less progressive tax code, may cause more tax minimisation activities. It follows that the frequently-advocated policy of reducing the highest tax rate may fail as a policy directed at improving tax discipline. One way of offsetting the possible harm to tax compliance from a less progressive tax could be an adjustment of the penalty and monitoring functions.