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We provide new results on the sphere demodulator (SD) and its new variant, the list sphere demodulator (LSD). A new reduced complexity SD algorithm is presented. We suggest implementing the necessary sorting of constellation symbols through a look up table. In addition, we propose the use of a modified QR algorithm which tries to begin the search in the layers which are "easier to demodulate". These improvements also apply to the recently published soft output LSD, in which we implement the list using the heap structure.