The history of fair housing policy in the United States has fallen short of two of its primary objectives: Deconcentration of poverty and community desegregation. We compare distributions of Housing Choice Voucher (HCV) households at various scales to broader US distributions to better understand the program's successes and shortcomings. We find that HCV households at the nation-scale have been consistently more highly distributed among lower-Area Median Income (AMI) census tracts and racially or ethnically concentrated areas of poverty (RECAPs). We specifically consider the potential of affirmatively furthering fair housing within the HCV program to simultaneously boost overall distributions in higher-AMI census tracts and to decrease RECAP concentrations of HCV households, observing that targeted deployment of mobility-based interventions can significantly decrease the proportion of HCV households residing in RECAPs. We further consider the impact of small area fair market rents (SAFMRs) and state-level source-of-income protections on HCV household distributions, finding that both interventions may boost HCV households into higher-AMI census tracts.