A kit (100) for constructing a support surface (10) for a sleeping person. The kit (100) comprises: an air-permeable layer (20) having at least one pair of opposing layer-edge portions stretchable at least in the direction between the layer-edge portions (11, 12, 13, 14) to form the support surface; at least one pair of parallel opposing frame sections (30, 32, 34, 36) fixedly disposable at a distance therebetween for forming at least a portion of a frame (15) supporting the support surface; at least a first of said frame sections (30, 32, 34, 36) comprising a layer-edge engaging portion (31, 33, 35, 37) configured for fixedly engaging a corresponding layer-edge portion (11, 12, 13, 14); and a tensioning mechanism configured for moving the layer-edge engaging portion (31, 33, 35, 37) together with the layer-edge portion (11, 12, 13, 14) relative to the opposing frame section (30, 32, 34, 36) to at least partially tension the air-permeable layer (20) between the frame sections (30, 32, 34, 36).