A process is provided for recovering components from a low boiler mixture which is obtained in the distillation of hydrogenation effluents from the preparation of polymethylols, by multistage distillation of the low boiler mixture having a tertiary amine, water, methanol, a polymethylol, a methylolalkanal, an alcohol and an alkanal with a methylene group in the alpha position to the carbonyl group. A first distillation stage involves separating the low boiler mixture into a higher-boiling, predominantly water-rich fraction and into a lower-boiling aqueous organic fraction having the tertiary amine. A second distillation stage involves separating the aqueous organic fraction from the first distillation stage into a predominantly amine-containing fraction and a further amine-depleted fraction. The tertiary amine is trimethylamine or triethylamine and the bottom temperature in the second distillation stage is at least 110° C.