By using rate-compatible (RC) low density parity-check (LDPC) codes with adaptive modulation, we propose an adaptive, discrete-rate multiple-input multiple-output (MIMO) communications system. Given the high spectral efficiency of MIMO and the flexibility of an incremental redundancy (IR) protocol, combined with adaptive coding and modulation (ACM), the designed communications system is capable of achieving high data rates, for a low amount of overhead. A novel ACM power- and bit-allocation protocol is proposed to implement this system. We adapt the existing water-filling algorithm (WFA) to the discrete and finite bit rate constraints inherent in any communications system. This constrained WFA is shown to significantly improve the throughput performance of the communications system, over the case where a regular WFA is used. The results given in this paper show that the combination of IR and ACM with MIMO creates a wireless communications system that can easily adapt to channel fluctuations and provide high-data rates.