The pressure and temperature dependent viscosities of two glass forming liquids, glycerol and dibutyl phthalate (DBP), have been studied in the range P=0-3 GPa, T=0-125-degrees-C, and eta=10(1)-10(10) cP. These studies were made using a combination of a Tolling-ball and a centrifugal-force diamond anvil cell viscometer. The majority of the results extend up to viscosities of 10(7) cP, with those at 22.5-degrees-C going to 10(10) cP. The overall precision of the data are approximately 10% or better throughout. This level of precision allows us to define a viscosity surface which can then be extrapolated to the glass transition along both temperature and pressure cuts. The T-dependence of viscosity is larger for glycerol than DBP but the P-dependence smaller for glycerol than for DBP, whereas the T-dependence is much more pressure sensitive for DBP. These data provide an assessment of the T-dependence of an isothermal model (free volume), the P-dependence of an isobaric model (Vogel-Tammann-Fulcher) and by extension that for isochoric conditions. Fragility parameters are evaluated for these three isometric conditions. For glycerol and (less conclusively) DBP under isobaric conditions, the fragility increases markedly at high pressure. Under isochoric conditions, the fragility for both glycerol and DBP increases with increasing density. This is dramatic for DBP, which goes from a strong to an intermediate-strength liquid. For the isothermal model, we derive a new measure of fragility. Using this, DBP shows a trend common to several liquids, a decrease in fragility with increasing temperature. Glycerol, however, becomes more fragile over the same temperature range. For glycerol, the trends towards increased fragility at elevated pressure and temperature are consistent with diminished hydrogen bonding under those conditions. The P-dependence of the glass transition is also determined over a wide range of T. The slope, dT(g)/dP, is positive with the pressure dependence for glycerol being considerably smaller than for DBP; both are nonlinear, tending to saturate in temperature at high pressures.