We investigate optically the time-dependent concentration and mean fractional stretch of A-phage DNA molecules near a solid surface in a torsional shear flow, for solutions of DNA concentrations from 0.1c* to 3.0c*. At high Weissenberg number (Wi >= 10), the polymer migration caused by the hydrodynamic interaction with the surface diminishes as DNA concentration increases from 0.1c* to 1.0c*, indicating : a that screening of wall hydrodynamics occurs to some degree in the concentration range traditionally recognized as "dilute". In addition, the surface migration continues to exist in diminished form up to 3.0c*, implying that, while the chains are overlapping, they do not screen out the hydrodynamic interactions completely. On the time scale over which migration occurs, the apparent mean fractional stretch of DNA molecules decreases near the surface, which is probably caused by the selective retention of fragments near the surface as long chains migrate away.