In overtone singing, a melody is produced by selecting an appropriate voice harmonic, one after another, while keeping the fundamental frequency constant. A specific harmonic is selected by changing the shape of the oral cavity which functions as a resonator corresponding to the formant used in vowel production. In addition, attenuation of particular frequency components by antiresonance of the vocal tract seems to occur. Frequently, such suppressed spectral components are observed in the spectrogram, usually in the frequency region immediately above the selected frequency for the tune and sometimes, in skilled performers, in a lower region also. This suppression, presumably associated by additional poles coupled with the zeroes introduced, may perceptually enhance the tuned component. We suggest two hypotheses about the mechanism to produce the pole-zero pairs: one employs an acoustic branch cavity, and the other assumes nonlinear generation of additional sound source at the vocal tract constriction due to positive feedback involving turbulence and possibly wall vibration.