The present invention relates to a process for preparing a partially hydrogenated butadiene polymer comprising no more than 3 mol % 1,2-butadiene-recurring units (A) and no more than 3 mol % ethylene recurring units (D), calculated on the total content mol/mol of recurring units, wherein a butadiene polymer comprising 1,2-butadiene recurring units (A) and 1,4-butadiene recurring units (B) is hydrogenated in the presence of hydrogen and a titanium-, zirconium- and/or hafnium-based metallocene compound as hydrogenation catalyst and a cocatalyst, characterized in that: a) the hydrogenation catalyst has a reaction rate ratio of r1/r2 greater than 5, wherein r1 and r2 are the hydrogenation rates of recurring units (A) and (B) respectively at the same reaction conditions, b) the cocatalyst is an alkali metal hydride, added as such or prepared in situ, and c) hydrogenation of the conjugated diene is carried out until at least 97% of recurring units (A) have been hydrogenated.