Multi-dimensional (MD) mapping offers more flexibility in mapping design for bit-interleaved coded modulation with iterative decoding (BICM-ID) and potentially improves the bandwidth efficiency. However, for higher order signal constellations, finding suitable MD mappings is a very complicated task due to the large number of possible mappings. In this paper, a novel mapping method is introduced to construct efficient MD mappings to improve the error performance of BICM-ID over Rayleigh fading channels. We propose to break the MD mapping design problem into four distinct $2$-D mapping functions. The $2$-D mappings are designed such that the resulting MD mapping improves the BICM-ID error performance at low signal to noise ratios (SNRs). We also develop cost functions that can be optimized to improve the error performance at high SNRs. The proposed mapping method is very simple compared to well-known mapping methods, and it can achieve suitable MD mappings for different modulations including higher order modulations for BICM-ID. Simulation results show that our mappings significantly outperform the previously known mappings at a target bit error rate (BER) of $10^{-6}$. Our mappings also offer a lower error-floor compared to their well-known counterparts.