The discharge performance of a primary, bobbin-style electrochemical cell is improved by incorporating a separator formed from a continuous separator sheet defining a two-layer cylindrical sidewall and a closed bottom end between the included electrochemical cell cathode and anode. A first layer of the cylindrical separator is formed by rolling a first end of a continuous separator sheet into a cylinder having a central axis parallel with a longitudinal axis of the continuous separator sheet, and then rolling a second end of the continuous separator sheet around the exterior of the first cylindrical layer to form a second cylindrical layer. The closed bottom end is formed by a portion of the continuous separator sheet located between the rolled portion of the first end and the rolled portion of the second end.