An electrochemical cell is presented. The cell includes a housing having an interior surface defining a volume, and an elongated, ion-conducting separator disposed in the volume. The separator usually extends in a vertical direction relative to a base of the housing, so as to define a height dimension of the cell. The separator has a first circumferential surface defining a portion of a first compartment. The cell further includes a shim structure disposed generally parallel to the first circumferential surface of the separator between the interior surface and the first circumferential surface of the separator. The structure includes at least two shims, a first shim and a second shim, that substantially overlap each other. An energy storage device including such an electrochemical cell is also provided.