The advantages of the grafting-to approach for the formation of tethered polymer layers, or polymer brushes, include construction under ambient conditions, precise control of polymer molecular weight, and control of dispersity. These advantages are counterbalanced by the relatively low grafting density typically achieved. We developed a method, based on segmental adsorption and high solution concentration, for achieving significant increases in surface attachment density. The method can be used with substrates of any geometry and requires only a minimum of polymer solution. The experimental results revealed that there is a solution concentration, inversely related to molecular weight, above which there is no additional increase in tethered chain density. The surface attachment density was determined by two complementary techniques, solution depletion and ellipsometry, and consistent trends were found.