A tobacco smoke filter or filter element comprising: a longitudinally extending core which includes tobacco smoke filtering material; an outer wrapper engaged around the longitudinal extending core; wherein the longitudinally extending core includes one or more channels extending longitudinally upstream from the downstream end of the core wherein: (a) the longitudinally extending core includes a hollow tube of tobacco smoke filtering material which does not extend the full length of the core; or (b) the longitudinally extending core includes a downstream element comprising a longitudinally extending tube having a plurality of spaced ribs extending generally inwardly to a longitudinally extending inner body, the ribs defining a plurality of longitudinally extending channels therebetween; or (c) wherein the longitudinal extending core includes a downstream element comprising a longitudinally extending downstream core of tobacco smoke filtering material; a first air permeable inner wrapper engaged around the downstream core; and optionally a second inner wrapper engaged around the first inner wrapper; the first inner wrapper having a profiled (e.g. corrugated) outer surface which defines with the second inner wrapper or the outer wrapper at least one longitudinally extending channel which extends longitudinally upstream from the downstream end of the downstream core and which extends only part of the length of the downstream core; and wherein the downstream end of the outer wrapper and the downstream end of the first inner wrapper extends beyond the downstream end of the core around which is engaged to define a cavity at the downstream end of the filter. a longitudinally extending core which includes tobacco smoke filtering material; an outer wrapper engaged around the longitudinal extending core; wherein the longitudinally extending core includes one or more channels extending longitudinally upstream from the downstream end of the core wherein: (a) the longitudinally extending core includes a hollow tube of tobacco smoke filtering material which does not extend the full length of the core; or (b) the longitudinally extending core includes a downstream element comprising a longitudinally extending tube having a plurality of spaced ribs extending generally inwardly to a longitudinally extending inner body, the ribs defining a plurality of longitudinally extending channels therebetween; or (c) wherein the longitudinal extending core includes a downstream element comprising a longitudinally extending downstream core of tobacco smoke filtering material; a first air permeable inner wrapper engaged around the downstream core; and optionally a second inner wrapper engaged around the first inner wrapper; the first inner wrapper having a profiled (e.g. corrugated) outer surface which defines with the second inner wrapper or the outer wrapper at least one longitudinally extending channel which extends longitudinally upstream from the downstream end of the downstream core and which extends only part of the length of the downstream core; (a) the longitudinally extending core includes a hollow tube of tobacco smoke filtering material which does not extend the full length of the core; or (b) the longitudinally extending core includes a downstream element comprising a longitudinally extending tube having a plurality of spaced ribs extending generally inwardly to a longitudinally extending inner body, the ribs defining a plurality of longitudinally extending channels therebetween; or (c) wherein the longitudinal extending core includes a downstream element comprising a longitudinally extending downstream core of tobacco smoke filtering material; a first air permeable inner wrapper engaged around the downstream core; and optionally a second inner wrapper engaged around the first inner wrapper; the first inner wrapper having a profiled (e.g. corrugated) outer surface which defines with the second inner wrapper or the outer wrapper at least one longitudinally extending channel which extends longitudinally upstream from the downstream end of the downstream core and which extends only part of the length of the downstream core; and wherein the downstream end of the outer wrapper and the downstream end of the first inner wrapper extends beyond the downstream end of the core around which is engaged to define a cavity at the downstream end of the filter.