This letter establishes the computational complexity savings that a properly positioned single bit of feedback can provide in the computationally intense setting of quasi-static MIMO communications. Specifically, this letter identifies novel practically constructed feedback schemes and explicit and non-random multiple-input multiple-output (MIMO) encoding-decoding schemes that, in the presence of a single bit of feedback, jointly guarantee the optimal diversity-multiplexing tradeoff (DMT) with a polynomial time complexity. Going one step further, this letter also presents an opportunistic communication scheme that, at all rates including rates close to the maximum multiplexing gain, can provide near-ergodic reliability at just polynomial time computational complexity costs. This is the best known computational complexity that suffices to achieve near-ergodic reliability in the quasi-static MIMO settings.