Five sinuous valleys that begin near the margins of the Hesperian-aged Dorsa Argentea Formation (DAF) are examined using Mars Global Surveyor Mars Orbiter Laser Altimeter data. These valleys are carved into the surrounding Noachian cratered terrain and extend away from the DAF for lengths up to 1600 km before terminating in the Argyre basin 1--3 km below their starting elevations. The association of these valleys with the DAF, thought to be the volatile-rich deposits of a previously widespread circumpolar ice sheet, supports the scenario whereby the valleys formed contemporaneously with the DAF and served as conduits for drainage of meltwater associated with the melting and retreat of the ice sheet. Examination of the head regions of three of the valleys reveals pits and basins carved into the local deposits of the DAF closely associated with the valley heads. On the basis of the distribution of these pits and basins, their morphologies, size, spacing, and basal elevations similar to the nearby valleys, we conclude that the pits and basins represent the expression of the valleys within the DAF. We suggest that the pits and basins resulted from surface collapse of the deposits due to basal drainage of meltwater beneath the thinning ice sheet. Sinuous ridges within some of the basins appear similar to terrestrial eskers and further support this scenario.