A rubber composition is based on at least: from 60 to 100 phr of one or more diene elastomers, referred to as very low glass transition temperature (Tg) diene elastomers, exhibiting a Tg within a range extending from −110° C. to −70° C., chosen from butadiene homopolymers, copolymers of butadiene and of vinylaromatic monomer, exhibiting a content of vinylaromatic unit of between 0% and 5% by weight, and the mixtures of these; a reinforcing filler; crosslinking system; and from 50 to 150 phr of at least one hydrocarbon resin predominantly composed of units resulting from α-pinene monomers, the resin exhibiting an aliphatic proton content of greater than 95%.