A plasticity-induced crack-closure model was used to study fatigue crack growth and closure in a thin-sheet 2024-T3 aluminum alloy under threshold and constant-Kmax testing procedures. Two methods of calculating crack-opening stresses were compared: one based on contact-K analyses and the other on contact crack-opening-displacement (COD) analyses. These methods gave nearly identical results under constant-amplitude loading but under load-reduction (threshold) simulations the contact-K analyses gave lower crack-opening stresses than the contact-COD method. Crack-growth load-reduction simulations showed that remote closure (crack surface contact away from the crack tip) can cause a rapid rise in opening stresses in the near threshold regime for low-constraint (plane-stress) conditions and high applied stress levels for both low and high stress ratios. Under low applied stress levels and high constraint (near plane-strain) conditions, a rise in crack-opening stresses was not observed near the threshold regime. But the residual crack-tip-opening displacements (CTOD) were of the order of measured oxide thicknesses in the 2024 alloy. In contrast, under constant-Kmax testing, the CTOD near threshold were an order-of-magnitude larger than measured oxide thicknesses. Residual-plastic deformations were much larger than the expected oxide thicknesses. Thus, residual-plastic deformations, in addition to oxides and roughness, play an integral part in threshold development.