In long-range percolation on the integer lattice, for each pair of points $ \{ x, y \}$, there is an open edge between these points with probability depending on the Euclidean distance between the points, independent of all other edges. When are the long edges necessary for the existence of an infinite cluster? The truncation problem asks whether one can remove all long enough edges while still retaining an infinite open cluster. We discuss this question in the non-summable regime in dimensions $d\geq 3$. Here we show that the truncation problem has an affirmative answer.