A composition of a positive integer n is a finite sequence of positive integers a1, a2, …, ak such that a1+a2+⋯+ak=n. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more at position i, if ai+1 ≥ai+d. We study the average position, initial height and end height of the first ascent of size d or more in compositions of n as n →∞.