In previou work (Rotunno et al., JAS, 1988; Weisman et al., JAS, 1988), a theory was put forth, based on the analysis of idealized two- and three-dimensional simulations, that squall line strength and longevity was most sensitive to the strength of the component of low-level(0-3 km AGL) vertical wind shear perpendicular to squall line orientation. An ``optimal'' state was proposed, based on the relative strength of the circulation associated with the storm-generated cold pool and the circulation associated with the ambient shear, whereby the deepest leading edge lifting and most effective convective retriggering occured when these circulations were in near balance. Since these studies, many subsequent studies have brought into question the relevance of such an optimal state to observed squall lines, noting the existence of strong, long-lived systems in sub-optimal conditions and raising the question of the potential role of deeper-layer shears in promoting system strength and longevity in such situations. In the present paper, we revisit the issue of the role of shallow versus deep shear in promoting squall line strength and longevity through an analysis of an extensive set of 2D and 3D simulations, and reestablish the primary role of the low-level shear in this regard. We also demonstrate again that a wider range of environments than strickly ``optimal'' support significant squall lines in the simulations, as is also evident from observations, and clarify the dependence of squall line properties on both the strength and depth of the ambient shear.