In this paper, we propose 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. For U IFFTs, GreenOFDM provides better PAPR reduction capabilities than SLM-OFDM as it increases the number of waveform candidates from U (for SLM-OFDM) to U2/4. In this work, we propose an extension of the GreenOFDM that further increases the number of waveform candidates by a factor of 4 (from U2/4 to U2), 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. Furthermore, exciting methods for additional complexity reduction are also implemented and discussed.