Design studies for a low-aspect-ratio, large next-generation stellarator, Advanced Toroidal Facility II (ATF-II), with high-current-density, high-field, stable NbTi/Cu helical windings are described. The design parameters are an average plasma radius of 0.52 m, a major radius of 2 m, and a field on axis of 4 to 5 T, with 10 to 15 MW of heating power. Such a device would be comparable in scope to other next-generation stellarators but would have roughly the same aspect ratio as the tokamaks without, however, the need for current drive to sustain steady-state operation. A number of low-aspect-ratio physics issues need to be addressed in the design of ATF-II, primarily compromises between high-beta capability and good confinement properties. A six-field-period Compact Torsatron is chosen as a reference design for ATF-II, and its main features and performance predictions are discussed. An integrated (beta capability and confinement) optimization approach and optimization of superconducting windings are also discussed.