A heat-expandable rubber layer is provided to an inner all of a pneumatic tyre when the tyre is in an uncured state. The rubber layer is expanded when the tyre is in a vulcanized state. Once expanded, the rubber layer is capable of reducing rolling noises of the tyre. The rubber layer includes an elastomer composition based on at least an elastomer, e.g., natural rubber or butyl rubber; a reinforcing filler, e.g., silica and/or carbon black; between 10 and 80 phr of a blowing agent, e.g., an azodicarbonamide compound; and between 10 and 50 phr of a hot-melt compound with a melting point between 70° C. and 150° C., e.g., urea. The combination of the blowing agent and the hot-melt compound, at recommended high contents, makes it possible to very greatly reduce an expansion ratio and therefore a thickness of the rubber layer once the pneumatic tyre is vulcanized, without affecting noise absorption properties provided by the blowing agent.