Equilibrium issues encountered in the design of the National Compact Stellarator Experiment (NCSX) are discussed, focusing particularly on equilibrium magnetic islands. Significant improvements have been made to the VMEC equilibrium code to deal with numerical challenges at the low aspect ratios characterizing the NCSX design. Modifications to the PIES code have increased its speed, allowing routine evaluation of flux surfaces for candidate configurations. An optimizer has been built around the PIES code for healing magnetic islands, modifying the coil shapes to suppress resonant components of the magnetic field while preserving desired physics and engineering properties. The modified coils produce improved flux surface quality for a range of configurations. Neoclassical effects, which are not included in the PIES calculations, are estimated using a cylindrical model and are found to further reduce island widths significantly.