In a MIMO MAC where the base station has fewer receive antennas than the transmit antennas of all users, sphere (lattice) decoding for the existing MIMO-MAC codes requires an exhaustive search of exponentially large size before processing the root of a sphere-decoding tree. In this paper, two coding schemes are proposed and are shown to yield a constant sphere-decoding complexity, independent of the numbers of users and transmit antennas. The schemes require a channel feedback, but only at an extremely low rate. The first scheme is based on user selection, and the second scheme selects jointly users and transmit antennas, using a fast antenna selection algorithm recently proposed by Jiang and Varanasi. It also involves a design of rate-assignments that maximizes the overall DMT performance. It is shown that both schemes yield DMT performances far superior to the optimal MIMO-MAC DMT without channel feedback in certain multiplexing gain regime. Simulation results confirm that in some cases the second proposed scheme can provide an astonishing SNR gain of 14:5 dB at outage probability 10-6 compared to the optimal coding schemes without feedback.