For an international sample of banks, we construct measures of a bank’s absolute size and its systemic size defined as size relative to the national economy. We then examine how a bank’s risk and return on equity, its activity mix and funding strategy, and the extent to which it faces market discipline depend on both size measures. We show that bank returns increase with absolute size, yet decline with systemic size, while neither size measure is associated with bank risk as implicit in the Z-score. These results are consistent with the view that growing to a size that is systemic is not in the interest of bank shareholders. We also find that systemically large banks are subject to greater market discipline as evidenced by a higher sensitivity of their funding costs to risk proxies, consistent with the view that they can become too large to save. A bank’s interest costs, however, are estimated to decline with bank systemic size for all banks apart from those with very low capitalization levels. This suggests that market discipline, exercised through funding costs, does not prevent banks from attaining larger systemic size.