One way of improving the surface radiation-condition approach might be to use a condition higher than the second order. Here, this possibility is examined. For this purpose, surface radiation conditions higher than the second order are derived by a method which is, to a certain extent, similar to the method introduced by Jones (1988, IMA J. Appl. Math. 41, 21-30). It is shown that the first- and the second-order conditions are identically equal to the corresponding conditions given by Jones. Then, the third- and the fourth-order conditions, together with conditions obtained by the mode-annihilation method are tested against the second order, and exact results are given for an impedance sphere and for a penetrable sphere in a variety of circumstances. It has been observed that introduction of these higher-order radiation conditions from moderate to high frequencies improves the approximation considerably in comparison with results obtained by the use of a second-order radiation condition, especially in cases in which creeping waves are less pervasive.