Sheet-like products, such as tissue products, are disclosed containing an additive composition. The additive composition, for instance, comprises an aqueous dispersion containing an alpha-olefin polymer, an ethylene-carboxylic acid copolymer, or mixtures thereof. The alpha-olefin polymer may comprise an interpolymer of ethylene and octene, while the ethylene-carboxylic acid copolymer may comprise ethylene-acrylic acid copolymer. The additive composition may also contain a dispersing agent, such as a fatty acid. The additive composition may be incorporated into the tissue web by being combined with the fibers that are used to form the web. Alternatively, the additive composition may be topically applied to the web after the web has been formed. The additive composition can improve various properties of the sheet-like product. For instance, in one embodiment, the additive composition can reduce lint and increase softness.