This study explores whether the concentration-stability relation is affected by the level of analysis; i.e., bank-level versus country-level stability. The diverging results in the literature suggest that we may indeed expect differences between the two levels. With the z-score as the measure of financial stability, our theoretical analysis confirms that we may find such differences. Yet our empirical analysis for the EU-25 during the 1998-2014 period finds no economically significant effect of concentration on either the bank-level or the country-level z-score. The finding that concentration hardly affects stability at both levels of analysis is an indication of robustness in the empirical concentration-stability relation not previously established in the literature. This finding further suggests that neither supervisory restructuring, nor normal market-driven mergers, are likely to be substantially harmful to financial stability.