The shell trajectory is an existing method that is used to acquire MR data. Although to date it has not been as widely used as other methods (e.g., Cartesian acquisition, radial acquisition, or spirals) it has advantages for motion correction and for MR angiography with contrast agents. The current invention is a method to accelerate the shell acquisition by selectively omitting some of the data acquisition (i.e., under-sampling), with minimal impact on image quality. The shell trajectory acquires concentric spherical shells of raw data. In order to avoid image artifacts, the spacing between the sampled points must not be greater than the inverse of the field of view. With under-sampling, some data acquisitions (i.e., interleaves) that make up from the outer shells are omitted. Under-sampled methods are valuable if the artifacts that are generated do not interfere with the structure of interest, and this is shown to be the case. Under-sampling in radial acquisitions has become a very active area of development in MRI and the current invention could generate similar interest.