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A new framework for efficient exact maximum-likelihood (ML) decoding of spherical lattice codes is developed. It employs a double-tree structure: The first is that which underlies established tree-search decoders; the second plays the crucial role of guiding the primary search by specifying admissible candidates and is our present focus. Lattice codes have long been of interest due to their rich structure, leading to decoding algorithms for unbounded lattices, as well as those with axis-aligned rectangular shaping regions. Recently, spherical Lattice Space-Time (LAST) codes were proposed to realize the optimal diversity-multiplexing tradeoff of MIMO channels. We address the so-called boundary control problem arising from the spherical shaping region defining these codes. This problem is complicated because of the varying number of candidates to consider at each search stage; it is not obvious how to address it effectively within the frameworks of existing decoders. Our proposed strategy is compatible with all sequential tree-search detectors, as well as auxiliary processing such as the MMSEGDFE and lattice reduction. We demonstrate the superior performance and complexity profiles achieved when applying the proposed boundary control in conjunction with two current efficient ML detectors and show an improvement of 1dB over the state-of-the-art at a comparable complexity.