Time-frequency (T-F) masks represent powerful tools to increase the intelligibility of speech in background noise. Translational relevance is provided by their accurate estimation based only on the signal-plus-noise mixture, using deep learning or other machine-learning techniques. In the current study, a technique is designed to capture the benefits of existing techniques. In the ideal quantized mask (IQM), speech and noise are partitioned into T-F units, and each unit receives one of N attenuations according to its signal-to-noise ratio. It was found that as few as four to eight attenuation steps (IQM 4 , IQM 8) improved intelligibility over the ideal binary mask (IBM, having two attenuation steps), and equaled the intelligibility resulting from the ideal ratio mask (IRM, having a theoretically infinite number of steps). Sound-quality ratings and rankings of noisy speech processed by the IQM 4 and IQM 8 were also superior to that processed by the IBM and equaled or exceeded that processed by the IRM. It is concluded that the intelligibility and sound-quality advantages of infinite attenuation resolution can be captured by an IQM having only a very small number of steps. Further, the classification-based nature of the IQM might provide algorithmic advantages over the regressionbased IRM during machine estimation. V