This invention relates to a cooling segment for an aerosol-generating article comprising: a multilayer paper tube (6, 7, 8), comprising at least: a first paper tube layer (6), a second paper tube layer (8), surrounding coaxially said first paper tube layer (6), wherein, said cooling segment also comprises: a glue layer (7): sandwiched between said first paper tube layer (6) and second paper tube layer (8), made of: at least one first glued zone (1, 11, 12), with a glue amount per surface above a first threshold T1, extending along a first longitudinal portion (lp11, lp12) of said cooling segment (9), at least one lowly glued zone (2), with a glue amount per surface below a second threshold T2 which can be as low as zero, with T2