Rational approximations to the exponential function with denominator (1−λz−μz ²) ^s arise as stability functions of second derivative generalizations of Runge–Kutta methods. The purpose of this paper is to derive order barriers for approximations of this and related forms. Although some of these barriers are already known, we will analyse them in a new way. Order arrows were originally proposed as a complement to order stars for establishing barriers for A-stable methods but they are shown also to be a powerful tool for analysing the type of order barrier considered in this paper.