The reaction path leading to the partial and total reduction of alkynols and alkyndiols with general formula R–CH₂–CC–CH(OH)–R′ and R–CH(OH)–CC–CH(OH)–R′ (R, R′ = H, CH₃) on a D_3h symmetry Pd₉ cluster where atomic hydrogen is available have been analyzed by means of calculations based on density functional theory. The results, analyzed and discussed in atomistic details, suggest that small palladium clusters could be selective on the partial hydrogenation of triple bonds. The first energy barrier for the hydrogenation of the alkene derivatives is in fact much higher than the one corresponding to the hydrogenation of the triple bond. Further, the products of the partial hydrogenation, also when adsorbed on the Pd₉ cluster, are largely more stable than the corresponding alkynol or alkyndiol parents.