Bit-interleaved coded modulation with iterative decoding (BICM-ID) is investigated for bandwidth efficient transmissions, where the error performance can be improved by employing a suitable symbol mapping. This paper first introduces a low-complexity regular mapping optimization for BICM-ID and 8PSK, for the purpose of finding the optimal mapping. Furthermore, the irregular mapping optimization is proposed for a closer approach to the channel capacity. The extrinsic information transfer (EXIT) chart analysis is aided for the proposed optimization algorithms to provide design guidelines of mappings. The bit error rate (BER) results demonstrate that the BICM-ID system with the proposed optimal irregular mapping outperforms the other mappings used for comparison, and yields about 0.5dB away from the channel capacity over the additive white Gaussian noise (AWGN) channel.