To test reactor fuel elements for their content of fissionable material and poison, it is desirable to have an assembly which has maximum sensitivity to a perturbation of fissionable absorber in the axial center line of the reactor. For normal sizes of thermal power reactor fuel elements, a graphite-moderated reactor is a suitable choice. The change in reactivity measured is the difference between the effect of changes in the fission and absorption parameters. For a bare core and uniform fuel distribution, maximum sensitivity to a fission-parameter-perturbation is obtained for a reactor which has a minimum critical mass. Maximum sensitivity to an absorber-parameter-perturbation is obtained for a reactor which has a minimum amount of total absorptions. Both the fission and absorption sensitivity reach a maximum when the critical mass is minimum. For a reflected core and uniform fuel distribution, the sensitivity to a fissionable absorber can be increased 22% over the bare core sensitivity. By introducing an internal and external reflector, the sensitivity to a fissionable absorber can be increased 30% over the externally reflected core and 56% over the bare core. For nonuniform fuel distribution, an expression is derived relating the effect of a perturbation in fission and absorption to reactivity. The problem of finding a fuel distribution ψ(r) to maximize this expression is analytically formulated. A parameter study was made for the same reactors as for the uniform fuel distribution cases. This was done by shifting more fuel towards the center or towards the edge of the core. No gain in fissionable absorber sensitivity was observed for either the bare or the externally reflected cores. However, the internally and externally reflected core showed a 10% increase in fissionable absorber sensitivity when more fuel was shifted towards the center.