We sought to assess formally the extent to which different control and elimination strategies for human African trypanosomiasis Trypanosoma brucei gambiense (Gambiense HAT) would exacerbate or alleviate experiences of societal disadvantage that traditional economic evaluation does not take into account. Justice-enhanced cost-effectiveness analysis (JE-CEA) is a normative approach under development to address social justice considerations in public health decision-making alongside other types of analyses. It aims to assess how public health interventions under analysis in comparative evaluation would be expected to influence the clustering of disadvantage across three core dimensions of well-being: agency, association and respect. As a case study to test the approach, we applied it to five strategies for Gambiense HAT control and elimination, in combination with two different other evaluations: a cost-effectiveness analysis and a probability of elimination analysis. We have demonstrated how JE-CEA highlights the ethical importance of adverse social justice impacts of otherwise attractive options and how it indicates specific modifications to policy options to mitigate such impacts. JE-CEA holds promise as an approach to help decision makers and other stakeholders consider social justice more fully, explicitly and systematically in evaluating public health programs.