We describe an algorithm that automatically finds the smoothest formant trajectories for short segments of speech. The method selects for each segment the smoothest from a number of alternatives. The smoothness criterion is based on the modeling of formant tracks with polynomial functions and uses both the c2 badness-of-fit as well as the variances of the polynomial coefficients. A great advantage with respect to other methods is that it is completely automatic and reproducible because of our new criterion that quantifies the smoothness of formant tracks. Applied to some speech corpora, the new method shows smaller spreading ellipses especially for male’s high back vowels. Keywords: formant frequency measurement, variable ceiling, polynomial approximation, smoothness