We experimentally test the impact of expanding access to basic bank accounts in Uganda, Malawi, and Chile. Over two years, 17 percent, 10 percent, and 3 percent of treatment individuals made five or more deposits, respectively. Average monthly deposits for them were at the 79th, 91st, and 96th percentiles of baseline savings. Survey data show no clearly discernible intention-to-treat effects on savings or any downstream outcomes. This suggests that policies merely focused on expanding access to basic accounts are unlikely to improve welfare noticeably since impacts, even if present, are likely small and diverse.