Switched reluctance machines (SRMs) have received increasing attention for their many potential uses, such as for wind power and electric vehicle (EV) drive systems. The Quasi-Z-source Integrated Multiport Converter (QZIMPC) was recently introduced to improve the reliability of the SRM driver through small capacitance values. It is not possible, however, to simultaneously energize and deenergize two SRM phases in QZIMPC. This phenomenon can significantly increase the commutation period which, in turn, degrades the performance of SRM; in addition, this causes high-voltage ripples on the converter’s capacitors. Two switching algorithms are introduced and applied in this paper, and their performance with SRM is investigated in terms of torque ripple and peak phase current. The algorithms are based on prioritizing the control command in the on-going and off-going phases to fulfill the required load torque, as well as to accelerate the commutation process where possible. This is achieved without the interference of high-level controllers, which include speed controllers and/or torque ripple minimization. Through the simulation results, a comparison between the two switching algorithms is presented to determine their potential to improve the SRM drive system’s performance.