Lack of uniqueness in the circuit elements of the 2 DOF Network model [E. A. G. Shaw, J. Acoust. Soc. Am. 87, 398--410 (1990)] for the two lowest violin cavity modes A0 and A1 is one difficulty in its application, e.g., Shaw provided three possible parameter sets with substantial variation among them. To provide constraints on the range of parameters, global fitting of a large database of A0 and A1 frequencies, and their upper bout--lower bout pressure ratios---obtained by adding measured quantities of water (up to 250 cm[sup 3]) to a flat-plated Al violin-shaped cavity (volume =1800 cm[sup 3]) and varying its orientation---produced an optimized set of parameters close to Shaw's preferred set. With this optimized set of parameters, it was possible to estimate: (1) the mutual inertance contribution to the f-hole inertance; (2) a volume dependence of the A0 mode frequency of f V-0.254 in good agreement with the experimental value of V-0.269; and (3) predictions of the effect of sliding, rotating, and flipping the f holes.