The present invention relates to a process for preparing high-functionality polyethers having a colour number of less than 500 Hazen, by converting tris(hydroxyethyl) isocyanurate (THEIC) and one or more difunctional alcohols and/or modifying reagents with the aid of acidic catalysts. The present invention further relates to high-functionality polyethers having a colour number of less than 10, obtainable by such a process, and to the use of these high-functionality polyethers as adhesion promoters, thixotropic agents, rheology modifiers of polymers, in printing inks, varnishes and coatings, or as monomers for production of polyaddition or polycondensation polymers.