Voice training techniques often make use of exercises involving partial occlusion of the vocal tract, typically at the anterior part of the oral cavity or at the lips. In this study two techniques are investigated: a bilabial fricative and a small diameter hard-walled tube placed between the lips. Because the input acoustic impedance of the vocal tract is known to affect both the shaping of the glottal flow pulse and the vibrational pattern of the vocal folds, a study of the input impedance is an essential step in understanding the benefits of these two techniques. The input acoustic impedance of the vocal tract was investigated theoretically for cases of a vowel, bilabial occlusion (fully closed lips), a bilabial fricative, and artificially lengthening the tract with small diameter tubes. The results indicate that the tubes increase the input impedance in the range of the fundamental frequency of phonation by lowering the first formant frequency to nearly that of the bilabial occlusion (the lower bound on the first formant) while still allowing a continuous airflow. The bilabial fricative also has the effect of lowering the first formant frequency and increasing the low-frequency impedance, but not as effectively as the extension tubes.