The invention relates to a sulfur-crosslinkable rubber mixture comprising a rubber blend composed of at least one solution-polymerized diene polymer A of high molecular weight and at least one solution-polymerized polymer B of low molecular weight, wherein at least one of polymers A and B has been functionalized at the chain end and/or along the polymer chain and/or at a coupling site with at least one group selected from epoxy groups, hydroxyl groups, carboxyl groups, silane sulfide groups, amino groups, siloxane groups, organosilicon groups, phthalocyanine groups and amino group-containing alkoxysilyl groups, 30 to 300 phr of at least one silica and 1 to 20 phf of at least one substance of formula I) as silane coupling agent (R1R2R3)Si—S4—Si(R3R2R1)  II) where R1, R2, R3 in the structure may be the same or different and may be selected from linear or branched alkoxy, cycloalkoxy, alkyl, cycloalkyl or aryl groups having 1 to 20 carbon atoms.