Mappings for square quadrature amplitude modulation (QAM) are investigated in terms of the achievable capacity in bit-interleaved coded modulation (BICM). In G. Caire et al. (1998) it is conjectured that Gray labelings maximize this capacity. However, Gray mappings are not unique and it can be shown that the conjecture cannot hold in general for QAM constellation sizes larger than 16. Based on the bit level capacities of mappings, structures determining capacity are analyzed. Construction guidelines leading to capacity maximizing Gray mappings are presented.