Maximising educational attainment is important for both individuals and societies. However, understanding of why some students achieve better than others is far from complete. Motivation and achievement data from a sample of 782 secondary-school students in New Zealand reveal that two specific types of outcome goals, namely "maximal levels of aspiration" and "minimal boundary goals," predict subsequent student achievement independently of mastery, performance goals, self-efficacy, student demographics and context variables including school type and time spent in out-of-school activities. In addition, our results underline that the relationships between these two specific outcome goals and achievement are moderated by the type of assessment tasks used to index achievement. Taken together, these findings demonstrate that understanding variability in students' academic performance can be significantly enhanced by taking into consideration individual differences in the strength of their maximal levels of aspirations and minimal boundary goals.