Coil placement errors break the axisymmetry of tokamak magnetic fields. The non-axisymmetries cause magnetic islands, which can enhance locked modes, decrease confinement and lead to disruptions. An algorithm is presented for calculating the currents in small correction coils so that specified islands caused by known magnetic field errors will be eliminated. Surface of section plots indicate that the calculated correction coil currents will substantially eliminate islands. A slight modification of the algorithm allows one to calculate correction coil currents which give rise to isolated islands of prescribed size and toroidal phase. Changing the toroidal phase would give rise to a rotating island, and rotating magnetic islands may be useful for plasma edge control