The present invention relates to a silica-containing rubber mixture produced from at least one rubber, one sulphur-containing alkoxysilane, one crosslinking agent, one filler, and optionally further rubber auxiliary products and from 0.1 to 15 phr of a polysulphide additive of the formula (I) A-S—(S)x—S—Y—S—(S)x—S-A  (I) where x is 0, 1 or 2, Y is an aliphatic, cycloaliphatic or aromatic group that is optionally substituted or else comprises heteroatoms and A is an optionally substituted hydroxyethyl, carboxyaryl, hydroxyaryl, carboxyalkyl or thionamide moiety, and comprises from 0.1 to 15 parts by weight, based on 100 parts by weight of rubber used, of 1,6-bis(N,N-dibenzylthiocarbamoyldithio)hexane (CAS No.: 151900-44-6).