The present invention relates in at least selected embodiments to novel or improved microporous battery separators for lithium rechargeable batteries and/or related methods of making and/or using such separators. A particular inventive dry process battery separator or membrane separator exhibits a thickness that is less than about 14 μm and has increased strength performance as defined by reduced splittiness. The mode of splitting failure has been investigated, and the improvement in splittiness quantified by a novel test method known as the Composite Splittiness Index (CSI).