Noise cancellation in an MRI environment is difficult due to the high noise levels that are in the spectral range of human speech. This paper describes a two-step method to cancel MRI noise that combines operations in both the time domain (correlation subtraction) and the frequency domain (spectral noise gating). The resulting filtered recording has a noise power suppression of over 100 dB, a significant improvement over previously described techniques on MRI noise cancellation. The distortion is lower and the noise suppression higher than using spectral noise gating in isolation. Implementation of this method will aid in detailed studies of speech in relation to vocal tract and velopharyngeal function.