An enhanced understanding of what predicts students' confidence, and what predicts specific cases of under-confidence or over-confidence, benefits educational practices and motivational theories. For secondary-school students in England, confidence expressed as self-concept was most strongly predicted by (intrinsic) interest, perceived encouragement (praise), and subject-comparisons for mathematics, and by praise, interest, and peer-comparisons for science, controlling for achievement and various other factors. The students' reported subject-comparisons, peer-comparisons, anxiety, interest, and (extrinsic) utility differentially predicted the self-concept beliefs of under-confident, accurate, and over-confident students in various ways. For example, for mathematics, higher utility predicted higher self-concept when over-confident (but not when under-confident). For science, lower subject-comparisons (science thought to be harder than any other subject) predicted lower self-concept when under-confident (but not when over-confident). Understanding what predicts someone's self-concept when they are under-confident or over-confident may help these confidence biases to be corrected by educators or even by the students themselves.