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A number of decoding schemes have been proposed for Layered Space-Time systems, such as the Ordered Successive Interference Cancellation and the Sorted QR Decomposition. We describe here a new addition to that group, increasing the performance of Layered Space-Time decoding by using the Sorted QR Decomposition technique to construct a list of constellations to be passed to a Maximum Likelihood decoder. This paper shows that signifcant performance improvement can be obtained for symmetric systems, where there is an equal number of transmit and receive antennas. It shows that the proposed scheme, has a roughly linear increase in complexity compared to SQRD. To overcome this increase in computational complexity, an adaptive system is described that has similar performance with reduced complexity.