We used configurational entropy theory to model the viscosity (η) of hydrous melts of NaAlSi3O8, haplogranite (SiO2-KAlSi3O8-NaAlSi3O8), and complex (natural) granite composition from available measurements and recently published configurational heat-capacity data. The equation log η = Ae + Be/TSconf(T), where Sconf is configurational entropy, reproduces viscosity data for individual samples as well as or better than the empirical three-parameter TVF equation (defined below), and has the advantage of being based on thermodynamic theory. The variables Ae, Be, and Sconf(Tg), where Tg is glass transition temperature, were parameterized as a function of water content for compilations of viscosity data for hydrous NaAlSi3O8, haplogranite, and peraluminous granite melts. With the simplest assumption of ideal mixing between silicate and water components, configurational entropy models with between 4 and 10 fitting parameters reproduce experimentally determined η-T-XH2O relationships significantly better than previous literature models based on empirical equations. Our preferred configurational entropy models have root-mean-square deviations of 0.26 log units for NaAlSi3O8 (n = 77), 0.16 log units for haplogranite (n = 55), and 0.28 log units for peraluminous granites (n = 79). The best statistical fits to the data sometimes require thermodynamically unlikely variations in Ae, Be, and Sconf(Tg) as a function of water content, however, such that further calorimetry data are needed to extract accurate thermodynamic information from viscosity data sets for hydrous melts.