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 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 compounds or at least one or more than one vinylaromatic compound 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 polymer solutions A and B, followed by stripping and drying, - 30 to 300 phr of at least one silica and - 1 to 20 phf of at least one blocked and/or unblocked mercaptosilane as silane coupling agent. - 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 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 compounds or at least one or more than one vinylaromatic compound 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 compounds or at least one or more than one vinylaromatic compound 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 polymer solutions A and B, followed by stripping and drying, - 30 to 300 phr of at least one silica and - 1 to 20 phf of at least one blocked and/or unblocked mercaptosilane as silane coupling agent.