The enhancement of noisy speech is important for applications involving human-to-human interactions, such as telecommunications and hearing aids, as well as human-to-machine interactions, such as voice-controlled systems and robot audition. In this work, we focus on reverberant environments. It is shown that, by exploiting the lack of correlation between speech and the late reflections, further noise reduction can be achieved. This is verified using simulations involving actual acoustic impulse responses and noise from the ACE corpus. The simulations show that even without using a noise estimator, our proposed method simultaneously achieves noise reduction, and enhancement of speech quality and intelligibility, in reverberant environments over a wide range of SNRs. Furthermore, informal listening examples highlight that our approach does not introduce any significant processing artefacts such as musical noise.