Experimental devices for the study of the physics of high beta (β ≳ 4%), low aspect ratio (A ≲ 4.5)stellarator plasmas require coils that will produce plasmas satisfyinga set of physics goals, provide experimental flexibility and bepractical to construct. In the course of designing a flexible coilset for the National Compact Stellarator Experiment, several innovations have been made that may be useful in future stellaratordesign efforts. These include: the use of singular value decomposition methods for obtaining families of smooth current potentials on distantcoil winding surfaces from which low current density solutions may beidentified; the use of a control matrix method for identifying whichfew of the many detailed elements of a stellarator boundary must betargeted if a coil set is to provide fields to control the essentialphysics of the plasma; the use of a genetic algorithm for choosing anoptimal set of discrete coils from a continuum of potential contours; theevaluation of alternate coil topologies for balancing the trade-offbetween physics objectives and engineering constraints; the developmentof a new coil optimization code for designing modular coils and theidentification of a `natural' basis for describing current sheetdistributions.