Recent large-scale wave flume experiments on sheet-flow sediment transport beneath Stokes waves show more onshore-directed sediment transport than earlier sheet-flow experiments in oscillating flow tunnels. For fine sand, this extends to a reversal from offshore- (tunnels) to onshore (flumes)-directed transport. A remarkable hydrodynamic mechanism present in flumes (with free water surface), but not in tunnels (rigid lid), is the generation of progressive wave streaming, an onshore wave boundary layer current. This article investigates whether this streaming is the full explanation of the observed differences in transport. In this article, we present a numerical model of wave-induced sand transport that includes the effects of the free surface on the bottom boundary layer. With these effects and turbulence damping by sediment included, our model yields good reproductions of the vertical profile of the horizontal (mean) velocities, as well as transport rates of both fine and medium sized sediment. Similar to the measurements, the model reveals the reversal of transport direction by free surface effects for fine sand. A numerical investigation of the relative importance of the various free surface effects shows that progressive wave streaming indeed contributes substantially to increased onshore transport rates. However, especially for fine sands, horizontal gradients in sediment advection in the horizontally nonuniform flow field also are found to contribute significantly. We therefore conclude that not only streaming, but also inhomogeneous sediment advection should be considered in formulas of wave-induced sediment transport applied in morphodynamic modeling. We propose a variable time-scale parameter to account for these effects.