Purpose: To develop and compare four 4D-CBCT reconstruction methods that correct for respiratory motion and enhance image quality. Methods: Four motion-compensation workflows were developed employing a combination of deformable image registration (DIR) and image reconstruction. Groupwise registration was used to simultaneously register all frames of a base Four-Dimensional Cone-Beam CT (4D-CBCT) FDK reconstruction to a reference frame, providing a 4D transformation. This 4D transformation expresses a respiratory motion model and was used to apply a deformation during the backprojection operation to create a motion-compensated reconstruction. Two variables were assessed: reference image of registration (fixed or mean frame) and inclusion or exclusion of the motion-compensated reconstruction step. Fixed frame registration refers to using an actual frame from the 4D image (end of inhalation) as the target image. Mean frame registration refers to using a per iteration-estimated average frame image instead. Image quality was assessed in one clinical case through tissue boundary sharpness, noise, and presence of view-aliasing artifact. Results: Diaphragm edge sharpness (DES) was defined as the slope of the intensity gradient along the lung-diaphragm boundary. DES relative to the base 4D-CBCT reconstruction improved by 26.8% using fixed-frame registration alone; 15.5% using fixed-frame with motion-compensated reconstruction; decreased by 2.9% using mean-frame registration alone; and improved by 12.2% using mean-frame with motion-compensated reconstruction. Noise was reduced in soft tissue by 8.7% and 75.8% for the fixed-frame registration and registration with motion-compensation methods, respectively, and by 8.8% and 77.7% for the corresponding mean-frame methods. Reductions in undersampling artifacts were visible for all four methods relative to the base reconstruction while retaining higher frequency spatial details (i.e. blood vessels). Conclusion: A data-driven approach combining groupwise registration and motion-compensation has the potential to improve 4D-CBCT image quality. Adding motion compensation after groupwise registration reduced sharpness somewhat but resulted in reduced noise and structural artifacts. This work was supported by the National Cancer Institute of the National Institutes of Health under Award Number R01CA166119. The authors have no conflicts of interest.