A cigarette includes lighting and mouth ends. It may include a smokable segment disposed at the lighting end. It also includes a mouth-end segment; an aerosol-generation system disposed between the lighting and mouth ends, which includes (i) a heat-generation segment adjacent the smokable segment, including a heat source configured to be activated by combustion of a smokable material and an insulation layer of a non-glass material that is woven, knit, or both, and (ii) an aerosol-generating segment with aerosol-forming material disposed between, but physically separate from, each of the heat generation segment and the mouth end; a piece of outer wrapping material that provides an overwrap around at least a portion of the aerosol-generating segment, the heat-generation segment, and at least a portion of the smokable segment; those segments being connected together by the overwrap to provide a cigarette rod; that is connected to the cigarette rod using tipping material.