In this paper, two selection schemes are proposed for coded transmission over multiple-input multiple-output (MIMO) multiple-access channels (MAC) to yield a much higher diversity-multiplexing gain tradeoff (DMT) performance. These schemes require a channel feedback, but at an extremely low rate. The first scheme is based on user selection and can be easily implemented in the existing MIMO-MAC systems. Upper bounds on the minimal computational complexity required by sphere decoders to decode DMT-optimal codes for this scheme as well as for MIMO MAC without feedback are given. It is shown that this scheme can offer both a much larger DMT and an exponential reduction on decoding complexity, compared with the latter. The second scheme selects jointly the users and their transmit antennas. It requires an additional design of rate assignments for performance optimization. A very general framework on the design of optimal rate assignments is thus provided. It is shown that this scheme can yield DMT performances far superior to the optimal MIMO-MAC DMT without channel feedback. The simulation results confirm that in some cases, this scheme can provide an astonishing SNR gain of 14.64 dB at outage probability 10-6 compared with the optimal MIMO-MAC coding schemes without feedback.