The concept of exchange-coupled media (each grain having a soft end whose exchange field helps to switch a hard end) has recently been generalized to allow a continuous gradation of anisotropy from soft to hard. We have recently shown that the "figure of merit" for such media xi=2E(b)/mu 0MsHsw, proportional to the ratio of the energy barrier E-b to the switching field H-sw, cannot exceed 4 for any anisotropy profile K(r). In the thin-wall limit (exchange constant A<KL2), it can be made to approach 4 by choosing a graded anisotropy K(z)proportional to z(2). In developing such a medium, it is important to be able to experimentally probe the anisotropy distribution. In this paper, we study one method for doing this, the hard axis loop. In the absence of exchange, the second derivative of this loop gives the distribution directly; we show that even in the presence of realistic exchange, this remains approximately true and the anisotropy distribution can be extracted from the hard axis loop. (C) 2008 American Institute of Physics.