Transmission computed tomography (TCT) has been shown to be an accurate method of acquiring non-uniform attenuation maps for single-photon emission computed tomography (SPECT) attenuation compensation. One commonly encountered problem, especially for convergent beam geometries, is image truncation. We describe two methods for reducing associated truncation artifacts, with the goal of improving SPECT attenuation compensation without unduly increasing imaging or reconstruction times: (i) the two-scan method, which reduces the degree of truncation by combining two short-duration, patient-shifted scans, and (ii) a quantitative extrapolation method, which fills in truncated projections accounting for the correct amount of attenuating medium in the slice. The methods are evaluated by imaging two phantoms on a fan beam TCT system. Projection sets are truncated to various degrees with software, and reconstructed images are compared to both untruncated filtered backprojection and iterative reconstructions of truncated data. A fundamental analysis of SPECT attenuation factors is performed, and attenuation compensation of a cardiac insert is analysed. Results indicate the two-scan method can effectively reduce the degree of truncation in many cases, and the quantitative extrapolation method greatly improves SPECT attenuation compensation over using truncated maps.