The performance of bit-interleaved coded modulation with iterative detection (BICM-ID) depends strongly on the chosen constellation mapping. In this paper, we present an EXIT chart analysis of a number of mappings that have been designed especially for BICM-ID. This analysis reveals that all these mappings inevitably yield a bit error rate floor, which cannot be overcome by increasing the number of iterations or other measures taken at the receiver side. In order to remove this error floor, we introduce an inner code based on differential encoding with code doping. This coding scheme is of low complexity and introduces no additional redundancy. Two detection schemes of different complexity and similar performance are presented. This enhanced BICM scheme is applied to V-BLAST and a new concept to iteratively mitigate the multi-stream interference is presented.