Typical receiver processing, targeting always the best achievable bit error rate performance, can result in a waste of resources, especially, when the transmission conditions are such that the best performance is orders of magnitude better than the required. In this work, a processing framework is proposed which allows adjusting the processing requirements to the transmission conditions and the required bit error rate. It applies a-posteriori probability receivers operating over multiple-input multiple-output channels. It is demonstrated that significant complexity savings can be achieved both at the soft, sphere-decoder based detector and the channel decoder with only minor modifications.