Viscosity data are reported for n-hexadecane (C16), n-octadecane (C18), and n-eicosane (C20) at pressures between (3 and 243) MPa and temperatures between (304 and 534) K. These extreme conditions are representative of those encountered in ultra-deep petroleum formations beneath the deepwaters of the Gulf of Mexico. The measurements are taken with a novel windowed Inconel rolling-ball viscometer designed by our team that is calibrated with n-decane. A comparison of the reported viscosity values with the available literature data that cover limited pressure and temperature ranges, shows that the mean absolute percentage deviation, delta, ranges between 1.1% and 4.8%. The reported data extend the database of viscosity to the high-temperature, high-pressure region where most gaps occur in the literature data for n-hexadecane and n-octadecane. To the best of our knowledge, the results for n-eicosane are the first reported viscosity values at pressures above 2 MPa over the entire temperature range. The viscosity results are modeled with the free volume theory model in conjunction with density values obtained using the Peng-Robinson equation of state (EoS) and the PC-SAFT EoS. The delta values obtained with this model range from 2.0% to 3.5%. The data are also correlated by a non-linear surface fit as a simultaneous function of temperature and pressure that yields delta values of 0.40%, 0.43%, and 0.38% for C16, C18, and C20, respectively. (C) 2014 Elsevier Ltd. All rights reserved.