We suggest a new technique for the enhancement ofsingle channel reverberant speech. Previous methods have used either waveform deconvolution or modulation envelope deconvolution. Waveform deconvolution requires calculation of an inverse room response, and is impractical due to variation with source or receiver movement. Modulation envelope deconvolution has been claimed to be position independent, but our research indicates that envelope restoration in fact degrades intelligibility of the speech. Our method uses the observation that the smoothed segmental spectral magnitude of the room response is less variable with position. This is used to estimate the reverberant component of the signal, which is removed iteratively using conventional noise reduction algorithms. The enhanced output is not perceptibly affected by positional changes.