Star polymers comprising (1) a structural fragment acting as a center, and (2) at least three groups radially bound to this center, wherein these groups (i) each have at least one polyether structural unit comprising a polyoxyalkylene chain consisting of either ethylene oxide units or both ethylene oxide and propylene oxide units, wherein the polyoxyalkylene chain has a maximum proportion of 50 wt. % of propylene oxide units, relative to the weight of the polyoxyalkylene chain, and (ii) each have at least one residue comprising: (a) at least one *—Si(OR)x(R′)3-x group, in which R and R′, independently of one another, denote a (C1 to C4) alkyl group, x denotes 1, 2 or 3; (b) at least one anionic group; (c) at least one quaternized nitrogen atom; or (d) combinations thereof; are suitable for improving synthetic colorings of coloring compounds on keratin-containing fibers.