An additive mixture useful as a flame retardant is described. The mixture is comprised of (i) a poly(bromophenyl)alkane having in the molecule in the range of 13 to 60 carbon atoms and in the range of two to four aryl groups and (ii) a poly(bromophenyl)bromoalkane having in the molecule in the range of 13 to 60 carbon atoms and in the range of two to four aryl groups, said poly(bromophenyl)bromoalkane being in an amount which is greater than 25 wt %, based on the total weight of the additive mixture. A facile process for making the poly(bromophenyl)bromoalkane is also described.