The effect of pressure on the dielectric relaxation of two polyhydroxy alcohols is examined by analysis of existing data on glycerol, together with new measurements on xylitol. The fragility, or T-g-normalized temperature dependence, changes with pressure for low pressures, but becomes invariant above 1 GPa. When compared at temperatures for which the alpha-relaxation times are equal, there is no effect of pressure (<1 GPa) on the shape of the alpha dispersion at higher temperatures. However, nearer T-g, pressure broadens the alpha peak, consistent with the expected correlation of fragility with the breadth of the relaxation function. We also observe that the alpha-relaxation peaks for both glycerol and xylitol show an excess intensity at higher frequencies. For xylitol, unlike for glycerol, at lower temperatures this wing disjoins to form a separate peak. For both glass formers, elevated pressure causes the excess wing to become more separated from the peak maximum; that is, the properties of the primary and excess intensities are not correlated. This implies that the excess wing in glycerol is also a distinct secondary process, although it cannot be resolved from the primary peak.