NOVELTY - A separator for a rechargeable battery, comprises a microporous membrane having an initial porosity of at least 10%, and retaining at least 25% of the initial porosity after thickness compression of at least 18%. The microporous membrane comprises at least two layers, where a first layer has an initial porosity of greater than or equal to 10%, and a second layer has a porosity different than the porosity of the first layer and a tensile strength, and/or puncture resistance, greater than the tensile strength, and/or puncture resistance, of the first layer.    USE - As a separator useful in a rechargeable battery (claimed); useful in a variety of devices, including portable computers, tablet displays, personal digital assistants, mobile telephones, motorized devices (e.g. personal or household appliances and vehicles), instruments, illumination devices (e.g. flashlights), and heating devices.    ADVANTAGE - The separator maintains porosity after thickness compression during electrochemical cell cycling. The rechargeable electrochemical lithium-ion cells have high charge capacity and can be repeatedly fully charged and discharged without having volume changes that build up large stresses in the cell, especially when the cells are confined to a battery case. In the battery, the volume increase associated with a swelling electrode is offset by a compressible separator, leading to a final separator thickness and porosity in the desired operational range, while minimizing the volume change of the entire cell. The pores of the separator offer a significant volume space to compensate for some of the swelling of the electrode(s), such as the negative electrode. Thus, the separator helps to reduce the internal stresses in a cell during lithiation and delithiation.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) a rechargeable battery comprising an negative electrode having a volume change greater than about eighteen percent after lithiation; and a separator having a volume change opposite that of the negative electrode, such that, the volume change of the negative electrode is at least partially offset by the volume change of the separator, resulting in a volume change of the battery that is less than twenty percent after at least one room temperature, charge-discharge cycle; and    (2) producing the battery involving sandwiching the separator between a positive electrode and a negative electrode; packaging the sandwich into a battery case; adding an electrolyte into the battery case; and sealing the battery case.