A device for combining filter segments with cigarette rod segments in a filter tip attachment machine for making cigarettes, comprising: - first feed means for feeding a succession of gummed connecting strips; - second feed means for feeding a succession of groups, each comprising at least one cigarette rod segment and one filter segment abutted against each other end to end; - a combining conveyor configured to receive the succession of groups from the second feed means in a first receiving station and to receive the succession of gummed connecting strips from the first feed means in a second receiving station located downstream of the first receiving station so that each gummed connecting strip is applied in flag-like manner on a respective group to connect the cigarette rod segment to the filter segment; - a rolling drum which is coupled to the combining conveyor to receive from the combining conveyor, at a release station, a succession of groups, each provided with a gummed connecting strip applied in flag-like manner, and which is configured to roll the gummed connecting strip round the group; compression means associated with the combining conveyor and acting downstream of the second, receiving station and upstream of the release station, along a predetermined trajectory from the second, receiving station to the release station, to produce compression between each group and the respective connecting strip applied in flag-like manner; characterized in that the combining conveyor is made in the form of a combining drum comprising a peripheral mantle provided with a plurality of suction flutes for receiving respective groups and with support sections, alternated with successive suction flutes, for supporting the free portions of the respective gummed connecting strips applied in flag-like manner, and wherein the compression means comprise a pressure belt having an active section which faces the peripheral mantle of the combining drum and configured to keep each gummed connecting strip pressed against the respective group for a predetermined angular part of the rotation of the combining drum. - first feed means for feeding a succession of gummed connecting strips; - second feed means for feeding a succession of groups, each comprising at least one cigarette rod segment and one filter segment abutted against each other end to end; - a combining conveyor configured to receive the succession of groups from the second feed means in a first receiving station and to receive the succession of gummed connecting strips from the first feed means in a second receiving station located downstream of the first receiving station so that each gummed connecting strip is applied in flag-like manner on a respective group to connect the cigarette rod segment to the filter segment; - a rolling drum which is coupled to the combining conveyor to receive from the combining conveyor, at a release station, a succession of groups, each provided with a gummed connecting strip applied in flag-like manner, and which is configured to roll the gummed connecting strip round the group; compression means associated with the combining conveyor and acting downstream of the second, receiving station and upstream of the release station, along a predetermined trajectory from the second, receiving station to the release station, to produce compression between each group and the respective connecting strip applied in flag-like manner; characterized in that the combining conveyor is made in the form of a combining drum comprising a peripheral mantle provided with a plurality of suction flutes for receiving respective groups and with support sections, alternated with successive suction flutes, for supporting the free portions of the respective gummed connecting strips applied in flag-like manner, and wherein the compression means comprise a pressure belt having an active section which faces the peripheral mantle of the combining drum and configured to keep each gummed connecting strip pressed against the respective group for a predetermined angular part of the rotation of the combining drum.