In this paper, we present a Wiener filtering (WF) approach for extraction of somatosensory evoked potentials (SEPs) from the background electroencephalogram (EEG), with sweep-to-sweep variations in its signal power. To account for the EEG power variations, WF is modified by iteratively weighting the power spectrum using the coherence function. Coherence-weighted Wiener filtering (CWWF) is able to extract SEP waveforms, which have a greater level of detail as compared with conventional time-domain averaging (TDA). Using CWWF, the components of the SEP show significantly less variability. As such, CWWF should be useful as an important diagnostic tool able to detect minimal changes in the SEP. In an experimental study of cerebral hypoxia, CWWF is shown to be more responsive to detection of injury than WF or TDA.