Local gradient coils can improve the performance of echo-planar, diffusion, and short TE imaging in the brain. A modified singular value decomposition algorithm, which allows the rapid optimization and comparison of designs, was employed to optimize head size gradient coils. A theoretical expression for the torque on a cylindrical coil is presented and used to design coils that are free from torque while pulsed within a magnetic field. Gradient coils of various lengths both with and without torque constraints were compared; although torque-free coils do not perform as well as unbalanced coils, asymmetric torque-balanced coils can achieve comparable homogeneity with only a modest increase in inductance and resistance. Both types of coils outperform body size gradient coils by a dramatic margin. A three-axis head gradient designed using these techniques was constructed and used for brain imaging on a clinical scanner.