Accurate measurement of formant frequencies is important in many studies of speech perception and production. Errors in formant frequency estimation by eye, using a spectrogram, or automatically, using linear prediction, have been reported to be as high as 60 Hz F0 < 300 Hz. This exceeds the typical auditory difference limens (DLs) for formant frequencies and is also greater than some of the variation that one would like to study, e.g., the acoustic effects of varying vocal effort. The problem becomes substantially worse when F0 is as high as 500 to 600 Hz, which is not uncommon in the speech of women and children at high vocal efforts. In comparison with ordinary linear predictive analysis, the method described here drastically reduces measurement errors, given that the formant frequency is not below or only slightly above F0 (which rarely happens in speech). It thus becomes possible to study formant frequency variation in speech material that hitherto could not be analysed meaningfully since the effects of interest were no larger than the probable errors in measurement.