A direct method is described for finding optimal coils, and `flexibility' coils are presented which have been determined by this method. The method proceeds straight to a coil design from the required vacuum magnetic configuration parameters for the desired plasma, rather than producing an intermediate `surface current' description. This allows engineering requirements to be faithfully reproduced. The method has been applied by implementing a perturbative vacuum rotational transform evaluator as an optimality criterion. The speed of this evaluation step allows a thorough exploration of the set of possible coil trajectories and permits a high degree of confidence in the optimality of the best candidate. It is shown that the flexible heliac winding is very near optimal for rotational transform generation.