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In an earlier paper, a selective-mapping type turbo coded OFDM scheme was proposed, for which the interleaver of the encoder of the turbo coding can be varied to reduce the associated PAPR (peak to average power ratio) while the transmission of side information is not needed. In this paper, we propose two modified versions of that scheme. For the first, the variation of the interleaver of the turbo encoder is replaced by the variation of the bit permutation of the turbo codeword. For the second, the variation of the interleaver of the turbo encoder is replaced by the variation of a maximum-length sequence which is added to the turbo codeword. These two modified schemes can provide better PAPR reduction capability.