The recent development of quantitative elastohydrodynamics makes the accurate description of the temperature, pressure, and shear dependence of viscosity extremely important. It has been customary for tribologists to expect a second Newtonian plateau to appear in any flow curve for a polymer-blended lubricant and, since viscometers at ambient pressure cannot reach such a plateau, procedures have been suggested to extrapolate to a second Newtonian from commercial high-shear viscometer data. Two examples of oils, characterized in pressurized thin-film Couette viscometers, are presented for which there is no second Newtonian. Extrapolation from ambient-pressure high-shear viscometer data, by fixing the second Newtonian viscosity at the viscosity of the base oil, is not useful. Apparently, the second Newtonian will not appear when the base oil begins to shear thin at the shear stress for which the second Newtonian inflection might appear.