An integral form of the one-speed neutron-transport equation is applied to the case of a neutron-detecting foil placed in a homogeneous medium with an initially non-isotropic neutron population. A series of numerical calculations have been carried out to investigate the effect on the self-shielding flux-depression factor of anisotropy in the initial undisturbed flux. The case of a square foil of gold placed in a light-water medium is investigated. It is found that the existence of anisotropy in the initial flux leaves the flux correction factor essentially unchanged. However, the presence of anisotropy implies spatial non-uniformity of the scalar flux. Thus, movement of the center of mass of a foil in a flux which has a gradient, or rotation of a foil in a flux which has a second derivative can alter the undisturbed flux and the disturbed flux to which a foil is exposed, though the flux correction factor remains unchanged.