The maximum plasma current in Doublet III is found to be limited by disruptions when the limiter safety factor is approximately two. However, because of the strong toroidal and shaping-field effects on the rotational transform at the outer plasma edge associated with a vertical elongation of 1.5 D-shape, the safety factor estimated from simple geometric considerations for D-shaped plasmas corresponds to values as low as 1.5. These discharges operate stably with considerably higher plasma current than most reactor design studies assume. These low-q discharges show excellent plasma performance: very flat spatial electron temperature profiles, high-density operation with eR/BT up to 7.8, and good energy confinement producing a volume-average β of up to 1% with Ohmic heating only. This operational regime appears to be applicable to future high-β tokamaks with D-shaped cross-sections.