In this paper, we devise a new convex optimization strategy to both reduce the peak-to-average power ratio (PAPR) and the PAPR variance of orthogonal frequency-division multiplexing (OFDM) symbols. There are three distinctions of our proposed method as compared to existing methods: 1) PAPR, error vector magnitude (EVM), and free subcarrier power overhead are constrained simultaneously; 2) the EVM constraint is root-mean-square EVM (RMS-EVM); and 3) an auxiliary parameter, t, is used to generate quasi-constant PAPR through our proposed binary search algorithm (here, quasi-constant refers to the condition that most OFDM symbols' PAPR values are within a small, preset neighborhood). Simulation results are provided to demonstrate the effectiveness of our approach in comparison to others we consider.