Cone-beam CT (CBCT), used to reduce setup error in radiotherapy, takes a sequence of about 670 two-dimensional X-rays acquired in a circular arc around the patient over two minutes and reconstructs a three-dimensional volume from these projections. Consequently, when tissues move significantly during the acquisition the resulting volume is blurry or contains streaks. The projections themselves, though, are sharp. One of the main areas of research with CBCT has been to attempt to reconstruct the motion from these projections by collecting them into respiratory-phase or amplitude bins and using these to reconstruct bin-specific volumes. A variety of mechanisms are employed to identify and record respiratory motion so that it can be correlated with the projections. Not all motion that occurs in the body can be correlated with respiration. The research question pursued in this thesis is whether motion can be identified in a binning process without prior knowledge or models of the motion. Nomenclature describing motion classes and a specific type of artefact are introduced. The distinctiveness of this artefact class is demonstrated and methods to mitigate it are proposed and evaluated. Several techniques are then used to reduce an intractable search space to a computationally feasible one. A unique application of PCA to the reconstruction process allows new kinds of search approaches to be considered including an exhaustive search which requires a protocol change and a multiple-restart hill-climbing search that can be used with existing protocols. Experiments with three classes of phantoms, including a novel animated physical phantom, show the effectiveness of the two search methods which are finally compared with each other.