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Block-based early termination has been proposed for depth-first based MIMO sphere decoders (SD) in order to provide throughput guarantees. We show in this letter that such termination incurs, even under simple tree and norm choices, significant overhead in the required number of iterations under realistic channel conditions due to the depth-first search's highly variable complexity (number of iterations to achieve a target performance). We propose the use of a constrained version of Dijkstra's metric-first search which exhibits indistinguishable performance while avoiding the impractical memory requirements of Dijkstra's search. We show that for a 4Ã4 64-subcarrier OFDM system, the proposed alternative achieves ~2x decrease in complexity as compared to the depth-first SD with block early termination for the same throughput guarantee.