A method for combining at least a first segment, specifically a cigarette rod segment with at least a second segment, specifically a filter segment, a filter tip attachment machine for making cigarettes, comprising the following steps:
- feeding a succession of gummed connecting strips;
- feeding a succession of groups, each comprising at least a first segment, specifically a cigarette rod segment with at least a second segment, specifically a filter segment, abutted against each other end to end, towards a first receiving station of a combining conveyor provided with suction flutes for accommodating respective groups;
- applying each of the gummed connecting strips in flag-like manner on a respective group in a second receiving station of the combining conveyor downstream of the first receiving station, so as to connect the first segment to at least one second segment;
- conveying a succession of groups, each provided with a gummed connecting strip from the second receiving station to a release station;
- rolling the succession of gummed connecting strips round the respective groups;
- wherein the method comprises a step of compressing each group with the respective gummed connecting strip on it by means of compression means and maintaining the compression along a predetermined trajectory from the second receiving station to the release station.