A composition of a positive integer n is a finite sequence of positive integers a₁, a₂, …, a_k such that a₁+a₂+⋯+a_k=n. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more if a_i+1 ≥a_i+d. We determine the mean, variance and limiting distribution of the number of ascents of size d or more in the set of compositions of n. We also study the average size of the greatest ascent over all compositions of n.