Spiral, radial, and other nonrectilinear k-space trajectories are an area of active research in MRI due largely to their typically rapid acquisition times and benign artifact patterns. Trajectory design has commonly proceeded from a description of a simple shape to an investigation of its properties, because there is no general theory for the derivation of new trajectories with specific properties. Here such a generalized methodology is described. Specifically, a multi-objective genetic algorithm ( GA) is used to design trajectories with beneficial flow and off-resonance properties. The algorithm converges to a well-defined optimal set with standard spiral trajectories on the rapid but low- quality end, and a new class of trajectories on the slower but high-quality end. The new trajectories all begin with non-zero gradient amplitude at the k-space origin, and curve gently outward relative to standard spirals. Improvements predicted in simulated imaging experiments were found to correlate well with improvements in actual experimental measures of image quality. The impact of deviations from the desired k-space trajectory is described, as is the impact of using different phantoms.