A one-ply paper tissue product and a method of making a one-ply paper product combining high strength and softness along with low sidedness. The paper tissue product exhibits a sidedness parameter of less than 0.3 preferably, less than 0.225, a tensile modulus of no more than 32 grams/percent strain, a GM MMD of no more than about 0.225, and a cross directional strength of at least 200 grams per 3 inches. In stratification tissues, these properties are obtained by control of stratification, particularly, chemical stratification and stratification of furnish when appropriate. The tissue has a sidedness parameter value of less than 0.3, preferably, about 0.15 to about less than 0.225. In homogenous tissue, these properties are obtained by adding a strength enhancing agent to separate furnish sources prior to the funish sources being combined, and further, optionally adding the softener to the nascent web.