The strong mesoscale velocity fluctuations (“eddies”) observed in the deep Gulf Stream region may be dynamically necessary to incorporate the Recirculation Gyres which account for the downstream increase in transport. The eddy-current interaction leading to entrainment is studied in a two layer quasi-geostrophic model with piecewise uniform potential vorticity. It is shown that the volume entrained by a bottom eddy of strength Γ*2 initially located near the edge of a bottom current depends mainly on the lateral shear s2 of this current, rather than on the much stronger shear of the upper layer. It is suggested that the “mean entrainment velocity” into an isopycnal layer of nearly uniform vertical thickness is proportional to (Γ*2s2)1/2, where Γ*2 (cm2/sec) is proportional to the integrated potential vorticity anomaly of the eddy.