We must anticipate that the day is approaching when details of nuclear weapons design and fabrication will become common knowledge. On that day we must be particularly certain that all special nuclear materials (SNM) are adequately accounted for and protected and that we have a clear understanding of the utility of nuclear materials to potential adversaries. To this end, this paper examines the attractiveness of materials mixtures containing SNM and alternate nuclear materials associated with the plutonium-uranium reduction extraction (Purex), uranium extraction (UREX), coextraction (COEX), thorium extraction (THOREX), and PYROX (an electrochemical refining method) reprocessing schemes. This paper provides a set of figures of merit for evaluating material attractiveness that covers a broad range of proliferant state and subnational group capabilities. The primary conclusion of this paper is that all fissile material must be rigorously safeguarded to detect diversion by a state and must be provided the highest levels of physical protection to prevent theft by subnational groups; no "silver bullet" fuel cycle has been found that will permit the relaxation of current international safeguards or national physical security protection levels. The work reported herein has been performed at the request of the U.S. Department of Energy (DOE) and is based on the calculation of "attractiveness levels" that are expressed in terms consistent with, but normally reserved for, the nuclear materials in DOE nuclear facilities. The methodology and findings are presented. Additionally, how these attractiveness levels relate to proliferation resistance and physical security is discussed.