This paper proposes an improvement to a recent Peak-to-Average-Power-Ratio (PAPR) reduction technique for Orthogonal Frequency Division Multiplexing (OFDM), the GreenOFDM. This technique, which is inspired by SeLected Mapping (SLM), generates several waveform candidates using a given number of Inverse Fast Fourier Transforms (IFFT), and selects the one with the lowest PAPR for the transmission of the OFDM symbol. In GreenOFDM, we show that for (U) IFFTs, it provides better PAPR reduction capabilities than SLM-OFDM as it increases the number of waveform candidates from U (available for SLM-OFDM) to U^2/4. In this work, we propose a simple and clever extension of the GreenOFDM that further increases the number of waveform candidates by a factor 4 (from U^2/4 to U^2), or equivalently reduces by a factor of 2 the number of IFFTs for a same PAPR performance. Compared to SLM-OFDM, the improved GreenOFDM technique reduces the complexity by requiring only the square-root of the number of IFFTs for a same PAPR reduction performance.