Concurrently fed into a reaction zone held at about 10° C. or less are brominating agent, aluminum halide catalyst, and a solution of anionic styrenic polymer having a GPC Mn about 2000-30,000. The components are in at least two separate feed streams. The feeds are proportioned to maintain (a) the amount of aluminum halide being fed at about 0.8 mole percent or less based on the amount of aromatic monomeric units in the polymer being fed, and (b) amounts of brominating agent and unbrominated polymer in the reaction zone that produce a final washed and dried polymer product containing about 60-71 wt % bromine. The catalyst is deactivated, bromide ions and catalyst residues are washed away from the reaction mixture, and the brominated anionic styrenic polymer is recovered and dried. The dried polymer has a volatile bromobenzene content of about 600 ppm (wt/wt) or less as well as other beneficial properties.