A new method for generating variance reduction parameters for strongly anisotropic, deep-penetration radiation shielding studies is presented. This method generates an alternate form of the adjoint scalar flux quantity, φ†Ω which is used by both CADIS and FW-CADIS to generate variance reduction parameters for local and global response functions, respectively. The new method, called CADIS-Ω, was implemented in the Denovo/ADVANTG software suite, and results are presented for a concrete labyrinth test problem. Results indicate that the flux generated by CADIS-Ω incorporates localized angular anisotropics in the flux effectively. CADIS-Ω outperformed CADIS in the test problem while obtaining correct results. This initial work indicates that CADIS-Ω may be highly useful for shielding problems with strong angular anisotropics. A future test plan to fully characterize the new method is proposed, which should reveal more about the types of realistic problems for which the CADIS-Ω will be suited.