The solution of a special type of deep penetration problem is obtained by coupling a deep-penetration forward calculation with a localized adjoint calculation. The system on which the calculation is performed consists of a target far removed from a radiation source. In the absence of the target, the system geometry is simple (i.e., one- or two-dimensional). The problem is to compute some effect of interest (e.g., reaction rate, flux, etc.) within the target. The problem solution consists of (a) a source-centered calculation of the radiation field with the target absent, (b) a target-centered adjoint calculation on the system with the source absent, and (c) a coupling of the above two calculations. The technique has been applied to fissile and non-fissile targets located at various distances from and having various orientations with respect to a unit isotropic point fission neutron source in an infinite air medium.