A can combustor comprising: a generally cylindrical housing having an interior, an axis, and a closed axial end, the closed axial end including means for introducing fuel to the housing interior; a generally cylindrical combustor liner disposed coaxially within the housing and configured to define with the housing respective radially outer passages (132, 134) for combustion air and for dilution air, and respective radially inner volumes for a combustion zone and a dilution zone, the combustion zone being disposed axially adjacent the closed housing end, and the dilution zone being disposed axially distant the closed housing end; and a impingement cooling sleeve coaxially disposed between the housing and the combustor liner and extending axially from the closed housing end for a substantial length of the combustion zone to a sleeve closed end, the sleeve having a plurality of apertures sized and distributed to direct combustion air against the radially outer surface of the portion of the combustor liner defining the combustion zone for impingement cooling, wherein the flow of combustion air and dilution air in the radially outer passages is generally axially toward the closed housing end, wherein the dilution air passage includes a plurality of dilution ports in the combustion liner for admitting dilution air radially into the dilution zone, wherein the combustor liner and the closed axial end are configured such that essentially all of the combustion air flows through the impingement cooling apertures prior to admission to the combustion zone, characterised in that the impingement cooling sleeve is configured to seal off the combustion air from the dilution air passage after the combustion air has traversed the impingement cooling apertures. a generally cylindrical housing having an interior, an axis, and a closed axial end, the closed axial end including means for introducing fuel to the housing interior; a generally cylindrical combustor liner disposed coaxially within the housing and configured to define with the housing respective radially outer passages (132, 134) for combustion air and for dilution air, and respective radially inner volumes for a combustion zone and a dilution zone, the combustion zone being disposed axially adjacent the closed housing end, and the dilution zone being disposed axially distant the closed housing end; and a impingement cooling sleeve coaxially disposed between the housing and the combustor liner and extending axially from the closed housing end for a substantial length of the combustion zone to a sleeve closed end, the sleeve having a plurality of apertures sized and distributed to direct combustion air against the radially outer surface of the portion of the combustor liner defining the combustion zone for impingement cooling, wherein the flow of combustion air and dilution air in the radially outer passages is generally axially toward the closed housing end, wherein the dilution air passage includes a plurality of dilution ports in the combustion liner for admitting dilution air radially into the dilution zone, wherein the combustor liner and the closed axial end are configured such that essentially all of the combustion air flows through the impingement cooling apertures prior to admission to the combustion zone, characterised in that the impingement cooling sleeve is configured to seal off the combustion air from the dilution air passage after the combustion air has traversed the impingement cooling apertures.