A porous polymer separator layer that exhibits a non-uniform cross-sectional thickness and a method of making the same are disclosed. The porous polymer separator layer may be made by a phase-separation process. This process involves precipitating the porous polymer separator layer from a film having a non-uniform cross-sectional thickness similar to that sought to be imparted to the resultant separator layer. An electrochemical battery cell for a secondary liquid-electrolyte battery may incorporate the disclosed porous polymer separator layer between a negative electrode and a positive electrode in a way that that helps maintain a more evenly distributed current density within the cell.