Tone is usually described by starting height and direction of movement, but in languages with a crowded tonal space, multiple tones can have similar contours. Even in languages with few tones, details of contour shape may be used by listeners for tone identification. This study examines the effectiveness of using coefficients from polynomial equations to explore small differences in pitch contour shape and to convey this information for statistical analysis. Pitch contours for three tones from Green Mong are used as test cases. All three tones have low falling contours, but each has a distinctive phonation type. Using coefficients, large numbers of tokens can be compared to find consistencies in contour shape within tone categories and differences across categories. Discriminant analyses using the coefficients as predictor variables show that all three tones can be identified at levels well above chance using pitch contour shape alone. Quadratic coefficients improve classification rates over linear coefficients. The results also suggest that phonation type plays the largest role in identifying creaky tones in Green Mong. This technique should prove useful for analysis and synthesis of pitch contours. It seems particularly useful for examining details of contour shape in languages with a crowded tonal space.