Magnetic ripple of 1% or more caused by discrete solenoid coils in the central cells of tandem mirrors may severely affect the MHD stability. The ripple amplitude can be reduced by an order of magnitude by ferromagnetic annuli inserted within the coils at the regions of ripple maxima. The inserts need not affect the accessibility, coil diameter, or capital cost, since large quantities of steel are required within the coils for the neutron blanket and shield. Design of the ripple correction is simplified and linearized by the cylindrical geometry and by the saturation of the ferromagnetic steel.