A new generation of high power gradient systems which allow much faster MR imaging as well as shorter echo times has recently become available. Some of these high-speed gradient systems impose limits on the percentage of time during which the gradient can change in amplitude (slewing duty cycle). While this limitation may be immaterial to many 2DFT and echo planar imaging methods, a traditional circular spiral trajectory is difficult to use on these systems because its gradient waveforms change during the entire course of the trajectory so that the slewing duty cycle during the readout period is 100%. We describe a piecewise-linear spiral trajectory which is composed of linear segments and rounded corners. This trajectory reduces the slewing duty cycle while maintaining the desirable imaging properties of circular spirals including interleaving by simple gradient rotation. For one representative example, the slewing duty cycle is reduced to 46%. A conventional gridding method was used for image reconstruction, but a new numerical algorithm to calculate the density compensation factor was required. Use of piecewise-linear spiral trajectories reduces the impact imposed by limited gradient slewing duty cycle.