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We consider soft multiple-input multiple-output (MIMO) detection for the case of block fading. That is, the transmitted codeword spans over several independent channel realizations and several instances of the detection problem must be solved for each such realization. We develop methods that adaptively allocate computational resources to the detection problems of each channel realization, under a total per-codeword complexity constraint. Our main results are a formulation of the problem as a mathematical optimization problem with a well-defined objective function and constraints, and algorithms that solve this optimization problem efficiently computationally.