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Soft X-ray spectro-tomography provides three-dimensional (3D) chemical mapping based on natural X-ray absorption properties. Since radiation damage is intrinsic to X-ray absorption, it is important to find ways to maximize signal within a given dose. For tomography, using the smallest number of tilt series images that gives a faithful reconstruction is one such method. Compressed sensing (CS) methods have relatively recently been applied to tomographic reconstruction algorithms, providing faithful 3D reconstructions with a much smaller number of projection images than when conventional reconstruction methods are used. Here, CS is applied in the context of scanning transmission X-ray microscopy tomography. Reconstructions by weighted back-projection, the simultaneous iterative reconstruction technique, and CS are compared. The effects of varying tilt angle increment and angular range for the tomographic reconstructions are examined. Optimization of the regularization parameter in the CS reconstruction is explored and discussed. The comparisons show that CS can provide improved reconstruction fidelity relative to weighted back-projection and simultaneous iterative reconstruction techniques, with increasingly pronounced advantages as the angular sampling is reduced. In particular, missing wedge artifacts are significantly reduced and there is enhanced recovery of sharp edges. Examples of using CS for low-dose scanning transmission X-ray microscopy spectroscopic tomography are presented.