This article presents the mathematical formulations of two Overmodulation Strategies (OSs) for two-level inverters. The OSs aim to minimize the Equivalent Total Harmonic Distortion (THDe) or the Equivalent Weighted THD (WTHDe) of the αβ reference modulation indexes accomplishing the desired fundamental frequency magnitude. Straightforward analytical forms using just the first π/6 radians were built to approximate the solutions given by numerical optimization. The proposed OSs were compared to the state-of-the-art OSs, verifying their optimal performance in the whole overmodulation range. Experiments with an RL load allow observing the inverter commutation's effect when implementing the proposed OSs for different switching frequencies.