A method for optimizing stellarator vacuum magnetic fields is introduced. Application of this method shows that the stochasticity of vacuum magnetic fields can be made negligible by proper choice of the coil configuration. This optimization is shown to increase the equilibrium &bgr; limit by factors of two or more over that of the simple, ‘‘straight’’ coil winding law. This method is general and ought to be applicable to other systems in which stochasticity (1) presents a problem, yet (2) is affected by the design parameters.