A heuristic design method for rapid volumetric magnetic resonance imaging data acquisition trajectories is presented, using a series of second-order cone optimization subproblems. Other researchers have considered non-raster data collection trajectories and under-sampled data patterns. This work demonstrates that much higher rates of under-sampling are possible with an asymmetric set of trajectories, with very little loss in resolution, but the addition of noise-like artefacts. The proposed data collection trajectory, Durga, further minimizes collection time by incorporating short un-refocused excitation pulses, resulting in above 98% collection efficiency for balanced steady state free precession imaging. The optimization subproblems are novel, in that they incorporate all requirements, including data collection (coverage), physicality (device limits), and signal generation (zeroth- and higher- moment properties) in a single convex problem, which allows the resulting trajectories to exhibit a higher collection efficiency than any existing trajectory design.