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X-ray fluorescence computed tomography (XFCT) is a synchrotron-based imaging modality employed for mapping the distribution of elements within slices or volumes of intact specimens. A pencil beam of external radiation is used to stimulate emission of characteristic X-rays from within a sample, which is scanned and rotated through the pencil beam in a first-generation tomographic geometry. The measurements so obtained can be represented as generalizations of the attenuated Radon transform. The range of angular scanning employed is the subject of some variability in the XFCT imaging community, as some groups rotate the object through a full 360deg, while others employ only a 180deg rotation. In both cases, the entire object is scanned through the beam at each projection view. The use of a 180deg rotation is sometimes justified by implicit reference to a well-known symmetry property of the Radon transform, but that symmetry does not hold for the attenuated Radon transform. In this work, we demonstrate that a full scan of the object at each view coupled with a 360deg rotation does contain a two-fold data redundancy. While the redundancy does not give rise to a simple symmetry condition as in the case of the Radon transform, we will show that it does indeed license the use of the 180deg scheme. However, we will also demonstrate that when there is a single external fluorescence detector, the redundancy also licenses a potentially more attractive reduced-scan scheme, in which the object is rotated through a full 360deg, but in which only the half of the object closest to the fluorescence detector is scanned at each projection view. This new scheme may permit both reduced imaging times and improved image quality.