In many Western countries, researchers have documented ambitious educational choices among students of immigrant origin, for example, the tendency to choose academically more demanding routes than others at given levels of school achievement (e.g. grades, GPA). While this may indicate integration, some warn against an ‘immigrant optimism trap’, because choosing more demanding tracks at lower levels of GPA may increase risks of non-completion. Using longitudinal Swedish population data (n ≈ 90,000), we estimate an upper secondary ‘ethnic completion gap’ of 12 per cent to the detriment of students of immigrant background. We then address the ‘trap hypothesis’ via two analyses. The first shows that if students of immigration background would make similar educational choices as other students at the same GPA, the completion gap would shrink by 3.4 percentage points. The second analysis, based on simulations, suggests that restricting admission to academic programmes based on prior GPA, would lead to a massive relocation of low- and mid-GPA students to—usually less demanding—vocational programmes, but would only reduce the completion gap by 2.2 percentage points. These changes must be considered marginal in view of the substantial restrictions of choice that either of these measures would entail. We conclude that completion gaps are not primarily a result of unfounded immigrant optimism, and that optimistic choices are likely to be a net positive for integration by improving the chances of immigrant youth to reach tertiary-level qualifications and professional occupations.