In this paper we propose a novel space division multiplexing (SDM) detection method. The proposed technique constitutes a list search method and may be regarded as an advanced extension of the sphere decoder (SD). Our method may be employed in the so-called over-loaded scenario, where the number of transmit antenna elements exceeds that of the receive antenna elements. Furthermore, it is suitable for high-throughput, non-constant modulus modulation schemes, such as 16 and 64-QAM. We introduce a series of optimization rules which facilitate a substantial reduction in computational complexity. More specifically, we demonstrate that the method proposed, which we refer to as the soft-output optimized hierarchy (SOPHIE)-aided SDM detector exhibits the near-optimum performance of log-MAP SDM detector in all considered scenarios. The associated computational complexity, which we control using two complexity-control parameters, is substantially lower than that imposed by all previously proposed methods