Mandatory regulations are published worldwide for the efficiency of line-operated electric motors. The small-sized single-phase induction motors (SPIMs) will not be off the hook in terms of efficiency, since new regulations are scheduled to be introduced regarding them no later than July 2023. By doing so, the efficiency of capacitor-run SPIMs will be forced to exceed the (currently) typical ratings and comply with the requirements of the IE3 (i.e., premium) efficiency class. Since this task is challenging, the already published research works investigated several design, control, and manufacturing aspects. Nevertheless, less attention has been devoted to the study of the rotor bar’s shape impact, both on the SPIMs’ efficiency and starting capability. This gap is filled in this work by examining rotor squirrel-cage configurations with eight different bar shapes for the case of a four-pole/1.0 HP capacitor-run SPIM. A sensitivity analysis, which involves the simultaneous variation of the bar’s cross-sectional area, run-capacitor value, and auxiliary to main winding turns ratio, is performed. The motor’s electromagnetic behavior is estimated through finite element analysis. Through the acquired results, useful directions toward the SPIMs’ efficiency enhancement are provided, while simultaneously conclusions—not found elsewhere—are drawn concerning performance quantities, such as the motor’s starting current, currents shift angle, particular losses, breakdown torque, etc.