To identify the causal relationship between health-care spending and infant health, we employ the following source of identifying variation: hospital crowdedness measured in its simplest form, by the number of infants born on a given day in a given hospital. The thought experiment is during a crowded time; infants receive less medical care because resource constraints are binding. Using detailed information on every birth in California from 2002 to 2006, we find that hospital crowdedness reduces spending for at-risk infants. Our main finding is that at-risk infants who had more intensive hospital stays because they were born on slow days fared no better than their busy day counterparts. Specifically, the mortality gains from additional spending are negligible, and additional spending increases unscheduled hospital readmission rates in the first year of life. Our findings are robust to alternative measures of crowdedness that account for hospital crowdedness on the days surrounding the birth. When we use alternative measures of treatment intensity (length of stay and delivery spending), we find similar results. Our results suggest that when forced to reduce the intensity of treatment, the health-care system does so in a way that does not harm health.