A sulfur-crosslinkable rubber mixture comprising - a rubber blend composed of - at least one solution-polymerized diene polymer A of high molecular weight, formed from at least one conjugated diene and optionally one or more vinylaromatic compounds, having a content of vinylaromatic compound(s) of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on any diene content present, having a glass transition temperature T g according to DSC of -100°C < T g < +20°C, having a molecular weight M w according to GPC of more than 350 000 g/mol and having a polydispersity PD of 1.1 < PD < 3 and - at least one solution-polymerized polymer B of low molecular weight, formed from at least one conjugated diene, or at least one conjugated diene and one or more vinylaromatic compound(s) or at least one or more than one vinylaromatic compound(s) having a content of vinylaromatic compound of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on any diene content present, having a glass transition temperature T g according to DSC of - 100°C < T g < +80°C, having a molecular weight M w according to GPC of 1300 g/mol < M w < 10 000 g/mol and having a polydispersity PD of 1 < PD < 1.5, 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 (multiple polymers may be attached to one functionalization 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, and wherein the rubber blend has been obtained by combining the polymer solutions of polymers A and B, followed by stripping and drying, and - a vulcanization system comprising at least one accelerator and elemental sulfur and/or at least one sulfur donor substance, where the molar ratio of accelerated sulfur is 0.18 to 5, where the total molar amount of sulfur consists of elemental sulfur and the sulfur released by the sulfur donor substances. - a rubber blend composed of - at least one solution-polymerized diene polymer A of high molecular weight, formed from at least one conjugated diene and optionally one or more vinylaromatic compounds, having a content of vinylaromatic compound(s) of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on any diene content present, having a glass transition temperature T g according to DSC of -100°C < T g < +20°C, having a molecular weight M w according to GPC of more than 350 000 g/mol and having a polydispersity PD of 1.1 < PD < 3 and - at least one solution-polymerized polymer B of low molecular weight, formed from at least one conjugated diene, or at least one conjugated diene and one or more vinylaromatic compound(s) or at least one or more than one vinylaromatic compound(s) having a content of vinylaromatic compound of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on any diene content present, having a glass transition temperature T g according to DSC of or at least one conjugated diene and one or more vinylaromatic compound(s) or at least one or more than one vinylaromatic compound(s) having a content of vinylaromatic compound of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on any diene content present, having a glass transition temperature T g according to DSC of - 100°C < T g < +80°C, having a molecular weight M w according to GPC of 1300 g/mol < M w < 10 000 g/mol and having a polydispersity PD of 1 < PD < 1.5, 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 (multiple polymers may be attached to one functionalization 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, and wherein the rubber blend has been obtained by combining the polymer solutions of polymers A and B, followed by stripping and drying, and - a vulcanization system comprising at least one accelerator and elemental sulfur and/or at least one sulfur donor substance, where the molar ratio of accelerated sulfur is 0.18 to 5, where the total molar amount of sulfur consists of elemental sulfur and the sulfur released by the sulfur donor substances.