Abstract Background Supply driven programs that are not closely connected to community demand and demand-driven programs that fail to ensure supply both risk worsening inequity. Understanding patterns of uptake of behaviors among the poorest under ideal experimental conditions, such as those of an efficacy trial, can help identify strategies that could be strengthened in routine programmatic conditions for more equitable uptake. WASH Benefits Bangladesh was a randomized controlled efficacy trial that provided free-of cost WASH hardware along with behavior change promotion. The current paper aimed to determine the impact of the removal of supply and demand constraints on the uptake of handwashing and sanitation behaviors across wealth and education levels. Methods The current analysis selected 4 indicators from the WASH Benefits trial— presence of water and soap in household handwashing stations, observed mother’s hand cleanliness, observed visible feces on latrine slab or floor and reported last child defecation in potty or toilet. A baseline assessment was conducted immediately after enrolment and endline assessment was conducted approximately 2 years later. We compared change in uptake of these indicators including wealth quintiles (Q) between intervention and control groups from baseline to endline. Results For hand cleanliness, the poorest mothers improved more [Q1 difference in difference, DID: 16% (7, 25%)] than the wealthiest mothers [Q5 DID: 7% (− 4, 17%)]. The poorest households had largest improvements for observed presence of water and soap in handwashing station [Q1 DID: 82% (75, 90%)] compared to the wealthiest households [Q5 DID: 39% (30, 50%)]. Similarly, poorer household demonstrated greater reductions in visible feces on latrine slab or floor [Q1DID, − 25% (− 35, − 15) Q2: − 34% (− 44, − 23%)] than the wealthiest household [Q5 DID: − 1% (− 11, 8%). For reported last child defecation in potty or toilet, the poorest mothers showed greater improvement [Q1–4 DID: 50–54% (44, 60%)] than the wealthier mothers [Q5 DID: 39% (31, 46%). Conclusion By simultaneously addressing supply and demand-constraints among the poorest, we observed substantial overall improvements in equity. Within scaled-up programs, a separate targeted strategy that relaxes constraints for the poorest can improve the equity of a program. Trial registration WASH Benefits Bangladesh: ClinicalTrials.gov, identifier: NCT01590095. Date of registration: April 30, 2012 ‘Retrospectively registered’.