We consider the question of the approximation of nonnegative functions by nonnegative splines of order k (degree > k > k ) compared with approximation by that subclass of nonnegative splines of order k consisting of all those whose B-spline coefficients are nonnegative; while approximation by the former gives errors of order h k {h^k} , the latter may yield only h 2 {h^2} . These results are related to certain facts about quasi-interpolants.