A thunderstorm cell is a region of upward motion driven by latent heating that is, in its mature phase, accompanied by a rain-cooled surface outflow. A squall line is a collection of thunderstorm cells existing along a line at the ground. The squall line may be short-lived (order of several cell lifetimes) or long-lived (order of many cell lifetimes); the cells may be weak (vertical velocity ~ 5-10 m/s) or strong (vertical velocity ~ 20-40 m/s). Numerical simulations have shown that, other things being equal, squall lines tend be short-lived and weak if the ambient shear is weak, and long-lived and strong if the shear is moderate. Rotunno, Klemp and Weisman (1988; RKW) noted that the ability of the surface outflow to lift boundary-layer air to its level of free convection is enhanced with low-level shear, and concluded that the cold-pool-shear interaction is a central element in understanding the strength and longevity of squall lines. RKW proposed a simple way of thinking about the this enhanced-lifting effect in terms of the vorticity dynamics of cold pools in ambient shear flow. Recent theories of cold pools in shear attribute importance to aspects of the vertical shear profile other than just those of the boundary-layer. We report here on new simulations of cold pools in shear using the vorticity-streamfunction equations which address effects of the vertical distribution of the ambient shear on the amount of lifting realized. These simulations show that the vertical lifting at the leading edge of the cold-pool is most sensitive to the low-level shear. The vorticity-streamfunction simulations provide a convenient framework to interpret these results in terms of the the original RKW vorticity-dynamics argument.