The decay rate of an Alfvén or plasma surface wave propagating along an inhomogeneous layer of plasma is calculated. The inhomogeneous profile is thin and odd, but otherwise arbitrary. The wave's decay rate is determined using two fundamentally different methods, the integro-differential equation approach of Sedláčk and the Sturm—Liouville expansion technique of Cally, and found by both to depend only on the slope of the Alfvén or plasma frequency profile at the ‘resonant point’, and not on other details of its shape. The result is verified numerically. This problem represents a good example with which to compare and contrast the two methods.