To confine plasma adequately in toroidal magnetic fields for nuclear f
usion experiments, it is essential to control the magnetic islands cau
sed by perturbations and non-axisymmetry inherent to stellarators. A m
ethod is introduced which enables the perturbation harmonics of the fi
eld line Hamiltonian (which determines the size of islands and the deg
ree of chaos) to be approximated quickly. The method is based upon qua
dratic-flux minimizing surfaces which pass directly through both the X
and O points of the island chains. Using a suitable measure of island
width, it is possible to utilize standard numerical optimization meth
ods to achieve desirable configurations. A major island chain in the H
-1NF heliac vacuum field has been made to both disappear and to reappe
ar with opposite phase. These results have significance for self-heali
ng phenomena and the method is generally applicable to all stellarator
s and 1 1/2-dimensional Hamiltonian dynamical systems.