Voice production is constrained by laryngeal physiology and physics. Such constraints may present themselves as principal dimensions that are shared among speakers in how they produce and perceive voice. In this study, we attempt to identify such principal dimensions in voice outcome measures and the underlying laryngeal control mechanisms in a three-dimensional computational model of voice production. A large-scale voice simulation was performed with parametric variations in vocal fold geometry, stiffness, glottal gap, and subglottal pressure. Principal component analysis was applied to data combining both the laryngeal control parameters and acoustic and aerodynamic voice outcome measures. The results showed two dominant dimensions of vocal control. The first dimension describes interaction between respiration and vocal fold adduction in a way that increases glottal flow amplitude and vocal intensity at the cost of decreasing high-frequency harmonic production. The second dimension mainly describes control of medial surface thickness and glottal closure, which allows simultaneous increase in vocal intensity and high-frequency harmonic production but also increases risk of vocal fold injury. A third dimension with a reduced weight describes control of the fundamental frequency. The importance of these principal control dimensions to vocal expression of emotion and vocal health is discussed.