A diesel fraction is purified by a process having two reaction stages and a stripping stage in a single vessel. Heteroatoms are removed in the first stage, to permit the use of a sulfur sensitive aromatics saturation catalyst in the second stage, to produce a purified diesel stock. The first stage liquid effluent is stripped in a stripping stage and then passed into the second reaction stage, in which it reacts with fresh hydrogen for aromatics removal. The second reaction stage produces a hydrogen-rich vapor effluent, which may provide all or a portion of the first stage reaction hydrogen. A noble metal catalyst is employed in the second stage. The diesel feed for the process may be one that has been at least partially refined with respect to either or both heteroatom or aromatics removal.