Spiral scanning gradient waveforms can be optimized with respect to blurring from off-resonance effects by minimizing the readout time. This is achieved by maximizing the gradient amplitude during the scan so that the edge of k-space is reached as quickly as possible. Gradient hardware constraints are incorporated by considering a circuit model for the gradient coil and amplifier. The optimized gradient waveforms are determined by a set of coupled differential equations. The resulting solutions have shorter readout time than solutions that do not consider the circuit model.