The invention relates to a cross-linked rubber composition for a tire tread having a Shore A hardness greater than 45 and less than 57, measured in accordance with Standard ASTM D 2240, wherein the composition comprises greater than 25 phr and up to 100 phr, of one or more diene elastomers each having a temperature Tg of between -75.degree. C. and -40.degree. C., less than 75 phr and down to 0 phr, of one or more diene elastomers each having a temperature Tg of between -110.degree. C. and -75.degree. C., from 5 phr to 35 phr, of at least one hydrocarbon plasticizing resin miscible in said elastomer(s), said resin having a Tg of between 10.degree. C. and 150.degree. C. and a molecular weight Mn of between 400 and 2000 g/mol, and from 5 phr to 35 phr of at least one synthetic or natural plasticizing compound which comprises at least one glycerol fatty acid triester, wherein an aggregate constituted by the fatty acid(s) comprises oleic acid in a mass fraction equal to or greater than 60%.