Hydrogen-bonded monohydroxy alcohols belong to unique group of materials that characterize with additional prominence the Debye relaxation peak occurring in dielectric loss spectra. This exponential relaxation process is accompanied by another faster, less pronounced and asymmetric structural relaxation process. The dominating, slower process can be classified as “strong”, while the faster one, commonly identified with structural relaxation, is “fragile”. Here we present direct observation of changes of fragility of the dominated process from strong-to-fragile temperature dependence of the relaxation times at elevated pressure in 2-ethyl-1-hexanol. For the highest pressure of 1.57 GPa, the fragility of the dominating process is almost the same as that for the structural one at ambient pressure. Our analysis of the dielectric spectra at different P−T conditions also reveals that the response function of the dominating process transforms from exponential to nonexponential behavior.