We consider the classic Allingham and Sandmo (1972) tax compliance problem in the context of the Choquet-Schmeidler Expected Utility (CSEU) model, using the Non-Extremal Outcome (NEO)-additive capacities proposed by Chateauneuf et al (2002), in which Knightian uncertainty (ambiguity) exists concerning the penalty rate faced in the case of an audit. Pessimistic incarnations of the CSEU model can yield much lower underreporting rates than its Expected Utility (EU) counterpart, and do so without the need for moral sentiments, social stigma or probability perception functions. We confirm previous results, obtained in other contexts, showing that ambiguity-aversion reinforces the incentive effects of risk-aversion. We define the concept of a Risk-preserving increase in ambiguity (RPIA), which allows us to consider a change in the distribution of penalty rates such that (i) a CSEU decisionmaker will perceive a change in her welfare, whereas (ii) an EU decisionmaker will not. We also present simulation results that support the view according to which ambiguity aversion explains the use of accounting firms in preparing tax returns. Finally, by modeling a simple game between the taxpayer and the Internal Revenue Service (IRS), we show that increasing ambiguity in the tax code will not be in the IRS's interest if the associated rise in the cost of auditing is sufficiently large. It is therefore likely that increasing complexity (and therefore ambiguity) will reduce tax receipts, even in the presence of ambiguity-averse taxpayers.