Respiratory motion remains a major challenge for whole-heart coronary magnetic resonance angiography (CMRA). Recently, iterative reconstruction has been augmented with non-rigid motion compensation to correct for the effects of respiratory motion. The major challenge of this approach is the estimation of dense deformation fields. In this work, the application of such a motion-compensated reconstruction is proposed for accelerated 3D Cartesian whole-heart CMRA. Without the need for extra calibration data or user interaction, the nonrigid deformations due to respiratory motion are directly estimated on the acquired image data. In-vivo experiments on 14 healthy volunteers were performed to compare the proposed method with the result of a navigator-gated reference scan. While reducing the acquisition time by one third, the reconstructed images resulted in equivalent vessel sharpness of 0.44 +/- 0.06 mm(-1) and 0.45 +/- 0.05 mm(-1), respectively.