Background: One major challenge in cardiovascular magnetic resonance is reducing scan times to be more compatible with clinical workflows. In 3D magnetic resonance imaging (MRI), strategies to shorten scan times mostly rely on ECG‐triggering or self-navigation for motion management, but are affected by heart rate variabilities or respiratory drifts. A similarity-driven multi-dimensional binning algorithm (SIMBA) was introduced for 3D whole-heart angiography from ferumoxytol-enhanced free-running MRI. This study explores acceleration limits using SIMBA, and its compressed-sensing extension extra-dimensional motion-compensation (XD-MC)-SIMBA, while preserving image quality. Methods: Data from 6-min free-running acquisitions of 30 congenital heart disease (CHD) patients were retrospectively undersampled to simulate 5-, 4-, 3-, 2-, and 1-min datasets. SIMBA and XD-MC-SIMBA reconstructions were applied. and the consistency of the data selection together with sharpness metrics were computed as a function of undersampling. Image quality was rated on a 5-point Likert scale. Shorter 3-minute acquisitions were prospectively acquired in nine CHD patients. Results: SIMBA's motion state selection was consistent across undersampling levels, with only 2 of 30 cases showing completely different selections. Image quality metrics decreased with increased undersampling, with SIMBA scoring lower compared to XD-MC-SIMBA. The diagnostic quality was good, with lower scores for 2- and 1-min datasets. Using XD-MC-SIMBA, 43% (31/72) of cases showed improved scores compared to SIMBA and 58% (7/12) of 1-min datasets improved to good or excellent quality. Conclusions: This study demonstrates that ferumoxytol-enhanced free-running MRI can be highly accelerated for 3D angiography in CHD.With the aid of compressed sensing, XD-MC-SIMBA supports the acceleration down to 3 minutes or less.