This paper proposes a new interpretation of Finite Set Model Predictive Control (FS-MPC) for inverters. This interpretation gives insights into the existing limitations of FS-MPC and suggests mitigation strategies. Consequently, significant improvements of FS-MPC performance are achieved, including elimination of steady state error, improved harmonic spectrum, reduced control delays, etc. The proposed new MPC interpretation also establishes relationships between various control schemes, including FS-MPC and PWM-MPC, FS-MPC and MPC with integral action, etc. Additionally, the paper proposes further embellishments to FS-MPC based on its more efficient and accurate implementation. The findings of the paper are supported by simulations and experimental results.