This paper reports results of further experimentation on a previously developed physical model of the vocal-fold mucosa [Titze et al., J. Acoust. Soc. Am.97, 3080–3084 (1995)]. The effects of vocal-fold thickness, epithelial membrane thickness, and prephonatory glottal geometry on phonation threshold pressure were studied. Phonation threshold pressures in the range of 0.13 to 0.34 kPa were observed for an 11-mm-thick vocal fold with a 70-μm-thick “epithelial” membrane for different “mucosal” fluid viscosities. Higher threshold pressure was always obtained for thinner vocal folds and thicker membranes. In another set of experiments, lowest offset threshold pressure was obtained for a rectangular or a near-rectangular prephonatory glottis (with a glottal convergence angle within about±3°). It ranged from 0.07 to 0.23 kPa for different glottal half-widths between 2.0 and 6.0 mm. The threshold for more convergent or divergent glottal geometries was consistently higher. This finding only partially agrees with previous analytical work which predicts a lowest threshold for a divergent glottis. The discrepancy between theory and data is likely to be associated with flow separation from a divergent glottis.