Together with the magnetic shear across the magnetopause, the solar wind Alfvén Mach number, MA∞ plays a central role in determining the structure of the magnetosheath. Recent theoretical modeling has shown, in particular, that as MA∞ decreases, the region adjacent to the sunward side of the magnetopause where the interplanetary magnetic field (IMF) exerts a strong influence on the flow (i.e., the so‐called “plasma depletion layer”), is no longer confined to a thin layer ∼ 0.3 Earth radii (RE) thick but occupies an increasingly larger fraction of the magnetosheath. Furthermore, the model predicts the possibility of a plasma depletion layer for low MA∞, irrespective of the size of the magnetic shear at the magnetopause. In this paper we study three examples of low latitude ISEE 2 passes through the dayside magnetosheath near noon: December 3, 1979; October 5, 1979; and November 11, 1979. In all three examples, MA∞ was lower than normal. During the December 3 pass (which we treat, qualitatively), we find evidence of a plasma depletion layer when the IMF was pointing south. On the other two passes (which we study quantitatively), the interplanetary magnetic field was strongly northward pointing, leading to low magnetic shear at the respective magnetopause crossings. The October 5 pass was under steady interplanetary conditions and we find good agreement between theory and data. Temporal variations of the interplanetary medium during the November 11 pass necessitated an extension of the steady state theory to encompass piecewise steady (on average) interplanetary conditions. Better agreement with the data results when the theory is extended further to correct the total pressure at the sunward side of the magnetopause by integrating the magnetic tension term across the layer. For wide plasma depletion layers, this correction can be substantial.