There is much discussion in the United States about exclusionary discipline (suspensions and expulsions) in schools. According to a 2014 report from the U.S. Department of Education's Office for Civil Rights, Black students represent 15% of students, but 44% of students suspended more than once and 36% of expelled students. This analysis uses seven years of individual infraction-level data from public schools in Arkansas. We find that marginalized students are more likely to receive exclusionary discipline, even after controlling for the nature and number of disciplinary referrals, but that most of the differences occur across rather than within schools. Across the state, black students are about 2.4 times as likely to receive exclusionary discipline (conditional on reported infractions and other student characteristics) whereas within school, this same conditional disparity is not statistically significant. Within schools, the disproportionalities in exclusionary discipline are driven primarily by non-race factors such as free- and reduced-price lunch (FRL) eligibility and special education status. We find, not surprisingly, that schools with larger proportions of non-White students tend to give out longer punishments, regardless of school income levels, measured by FRL rates. Combined, these results appear to indicate multiple tiers of disadvantage: race drives most of the disparities across schools, whereas within schools, FRL or special education status may matter more.