Truncation artifacts arise when the object being imaged extends past the scanned field of view (SFOV). The line integrals which lie beyond the SFOV are unmeasured, and reconstruction with traditional filtered backprojection (FBP) produces bright signal artifacts at the edge of the SFOV and little useful information outside the SFOV. A variety of techniques have been proposed to correct for truncation artifacts by estimating the unmeasured rays. We explore an alternative, iterative correction technique that reduces the artifacts and recovers the support (or outline) of the object that is consistent with the measured rays. We assume that the support is filled uniformly with tissue of a given CT number (for example, water-equivalent soft tissue) and segment the region outside the SFOV in a dichotomous fashion into tissue and air. In general, any choice for the object support will not be consistent with the measured rays in that a forward projection of the image containing the proposed support will not match the measured rays. The proposed algorithm reduces this inconsistency by deforming the object support to better match the measured rays. We initialize the reconstruction using the water cylinder extrapolation algorithm, an existing truncation artifact correction technique, but other starting algorithms can be used. The estimate of the object support is then iteratively deformed to reduce the inconsistency with the measured rays. After several iterations, forward projection is used to estimate the missing rays. Preliminary results indicate that this iterative, support recovery technique is able to produce superior reconstructions in the case of significant truncation compared to water cylinder extrapolation.