This paper presents an improved variable-band hysteresis current controller for a two-level three-phase voltage source inverter (VSI). The controller takes the average voltages of the phase-leg switched outputs as an approximation to the load back-EMF voltages, and uses these results to vary the hysteresis bands so as to maintain constant phase-leg switching frequencies. The switching frequency control process is then further refined by fine tuning the hysteresis band variations to synchronize the zero crossings of the phase-leg current errors with a fixed reference clock so as to achieve a nearest space vector switching sequence, which further ensures that the switched output spectrum has been optimized. Finally, a technique is proposed to replace the third phase-leg current regulator with a fixed-frequency open-loop pulse-width modulator, where its commanded reference is generated from the average switched output voltages of the other two phase legs. This avoids the hazard of the three independent hysteresis current regulators adversely interacting with each other in a conventional system, resulting from an overconstrained control problem with only two degrees of freedom. Additionally, this approach allows the linear modulation range to be increased by adding a common-mode third-harmonic component to the third phase-leg reference command signal.