Disk-shaped current distributions are useful tools in modeling the magnetospheres of Earth and other planets and have also been adapted for modeling the geotail. Such models usually start with an axisymmetric vector potential but many be modified to account for observed asymmetries, variable thickness, and warping in response to an inclined orientation of the planetary dipole axis. Models of this type until now have either lacked the ability to simulate a sharp inner edge of the current and to control accurately its falloff with distance or did not allow a simple analytical representation. Her existing methods will be reviewed, after which a new class of models which overcomes the above deficiencies and also allows the modeling of current disks of finite thickness flanked by current-free regions will be presented. ¿ American Geophysical Union 1994