  The main linacs of the ILC consist of nine-cell cavities based on the TESLA
design. In order to facilitate reaching higher gradients we have re-designed
the cavity shape. This leads to a reduction, comparable to several current
designs, in both the ratio of the surface electric field to the accelerating
field (Es/Ea) and the magnetic field to the accelerating field (Bs/Ea). The
bandwidth of the accelerating mode is also optimized. This new shape, which we
refer to as the New Low Surface Field (NLSF) design, bears comparison with the
Ichiro, Re-entrant and LSF designs.
