Excess harvesting power can threaten the long-term sustainability of fisheries. Indicators of excess harvesting capacity must include input–output-based estimates of economic production efficiency. The increasing use of drifting Fish-Aggregating-Devices (DFADs) has boosted fishing productivity in high-seas tuna fisheries, perhaps beyond the biological capacity of the stocks, and is an object of global debate. We carried out a Data Envelopment Analysis (DEA) of relative changes in production efficiencies of the French purse-seine fleet targeting tropical tuna in the western Indian Ocean using two fishing strategies: (1) on floating objects (FOB) and (2) free swimming schools (FSC) using tuna catch and effort data spanning 1992–2019. We show that FOB fishing evolved dramatically through time with an estimated change of 3.6%yr−1 (8.0%yr−1 2007–2019), in contrast to 2.1%yr−1 for FSC. While the efficiency level in combining and using inputs has barely changed for FOB fishing, it means that all the growth in productivity comes from technical change for this strategy. The dynamics is different for the FSC with a mixture of innovation and higher efficiency. Immediate plans to improve input-based management in this region are needed to prevent further risks of overfishing to yellowfin (Thunnus albacares) and skipjack (Katsuwonus pelamis) tunas.