To reduce the scan time in three-dimensional (3D) imaging, the authors consider alternative trajectories for traversing k-space. They differ from traditional 3D trajectories, such as 3DFT, in that they employ time-varying gradients allowing longer readouts and in turn a reduced scan time. Some of these trajectories reduce by an order of magnitude the number of excitations compared with 3DFT and provide flexibility for trading off signal-to-noise ratio for scan time. Other concerns are the minimum echo time and flow/motion properties. As examples, the authors show two applications: A 3D data set of the head (field of view of 30 x 30 x 7.5 cm and resolution of 1.5 x 1.5 x 1.5 mm) acquired in 56 s using a stack of spirals in 3D k-space; and a 3D movie of the heart (20 x 20 x 20 cm field of view, 2 x 2 x 2 mm resolution, and 16 time frames per cardiac cycle) acquired in 11 min using a cones trajectory.