Previous studies of wind-blown sand have considered either fully erodible or non-erodible soils, but the transport over sparsely sand-covered soils is still poorly understood. The quantitative modeling of this transport is important for the parametrization of Aeolian processes under low sand availability. Here we show, by means of particle-based numerical simulations, that the Aeolian sand transport rate Q scales with the wind shear velocity u∗ as Q = a.[1 + b . (u∗/u∗t − 1)] .√(d/g) . ρf. (u∗² − u∗t²), where u∗t is the minimal threshold u∗ for sustained transport, d is particle size, g is gravity and ρf is air density, while u∗t and the empirical parameters a and b depend on the sand cover thickness. Our model explains the transition from the quadratic to cubic scaling of Q with u∗ as soil conditions change from fully erodible to rigid and provides constraints for modeling Aeolian transport under low sand availability.