A secondary battery comprising carrier ions, a non-aqueous electrolyte and at least two electrochemical stacks in a stacked arrangement, the direction of stacking of the at least two electrochemical stacks relative to each other being in a direction that is orthogonal to a reference plane, the carrier ions being lithium, sodium or potassium ions, each of the electrochemical stacks comprising, in a stacked arrangement, cathode structures, current collectors, cathodically active material layers, separator layers, anode current collectors, and a population of microstructured anodically active material layers, the separator layers being disposed between the cathodically active material layers and the members of the population of anodically active material layers, the anode current collectors having an electrical conductance that is substantially greater than the electrical conductance of the microstructured anodically active material layers, the direction of stacking of the cathode current collectors, cathodically active material layers, separator layers, anode current collectors, and microstructured anodically active material layers within each of the at least two electrochemical stacks being parallel to the reference plane, the carrier ions having a direction of travel between the cathodically active material layers and the anodically active materials of each of the at least two electrochemical stacks that is generally parallel to the reference plane as the secondary battery is charged and discharged, the members of the population of microstructured anodically active material layers of each of the at least two electrochemical stacks having a height, HA, of at least 100 micrometers measured in a direction orthogonal to the reference plane, a front surface, a back surface, a thickness, T, measured from the front surface to the back surface, and a void volume fraction of at least 0.1, wherein the front and back surfaces are substantially perpendicular to the reference plane, the thickness, T, is at least 1 micrometer and measured in a direction parallel to the reference plane, and the microstructured anodically active material layers comprise a fibrous or a porous anodically active material, and wherein the lineal distance, DL, between at least two members of the population of microstructured anodically active material layers of each of the at least two electrochemical stacks, measured in a direction parallel to the reference plane, is greater than the maximum value of HA for the population within each such electrochemical stack.