It is well known that although the conventional sphere decoder (SD) achieves optimal maximum likelihood (ML) performance at a reduced complexity compared to the naive ML detector, the SD computational complexity varies with signal noise ratio (SNR) and is high in the low SNR region. This paper proposes a new idea to overcome these drawback that reduces the complexity significantly at a negligible performance loss. The main idea is to scale the search radius of the original SD by a factor that depends on the SNR. This factor tends to unity for high SNR, which means there is no performance loss for high SNRs. The resulting SD performs nearly-optimal ML detection over the whole range of SNRs, while keeping its complexity roughly constant. We give simulation results and theoretical analysis to confirm the advantages of the proposed SD. It is suitable practical implementation because of its effectively-reduced and almost-fixed complexity.