It is known that applying a time-frequency binary mask to very noisy speech can improve its intelligibility but results in poor perceptual quality. In this paper we propose a new approach to applying a binary mask that combines the intelligibility gains of conventional binary masking with the perceptual quality gains of a classical speech enhancer. The binary mask is not applied directly as a time-frequency gain as in most previous studies. Instead, the mask is used to supply prior information to a classical speech enhancer about the probability of speech presence in different time-frequency regions. Using an oracle ideal binary mask, we show that the proposed method results in a higher predicted quality than other methods of applying a binary mask whilst preserving the improvements in predicted intelligibility.