The tautomerism of 3- and 5-hydroxypyrazole is studied at the B3LYP, CCSD and G3B3 computational levels, including the gas phase, PCM-water effects, and proton transfer assisted by water molecules. To understand the propensity of tautomerization, hydrogen-bond acidity and basicity of neutral species is approached by means of correlations between donor/acceptor ability and H-bond interaction energies. Tautomerism processes are highly dependent on the solvent environment, and a significant reduction of the transition barriers upon solvation is seen. In addition, the inclusion of a single water molecule to assist proton transfer decreases the barriers between tautomers. Although the second water molecule further reduces those barriers, its effect is less appreciable than the first one. Neutral species present more stable minima than anionic and cationic species, but relatively similar transition barriers to anionic tautomers.