The present invention relates to a process for direct production of mixtures of short-chain high-functionality polyoxyalkylene polyols and long-chain low-functionality polyoxyalkylene polyols. The short-chain high-functionality polyoxyalkylene polyol component is obtained by alkylene oxide addition onto high-functionality H-functional starter compounds while the long-chain low-functionality polyoxyalkylene polyol component is correspondingly obtained by alkylene oxide addition onto low-functionality H-functional starter compounds. The invention further relates to the resulting polyoxyalkylene polyols and to the reaction thereof to produce polyurethanes.