A battery separator is a microporous membrane. The membrane has a major volume of a thermoplastic polymer and a minor volume of an inert particulate filler. The filler is dispersed throughout the polymer. The membrane exhibits a maximum Z-direction compression of 95% of the original membrane thickness. Alternatively, the battery separator is a microporous membrane having a TMA compression curve with a first substantially horizontal slope between ambient temperature and 125° C., a second substantially horizontal slope at greater than 225° C. The curve of the first slope has a lower % compression than the curve of the second slope. The curve of the second slope is not less than 5% compression. The TMA compression curve is graphed so that the Y-axis represents % compression from original thickness and the X-axis represents temperature.