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Lumpfish ( Cyclopterus lumpus ) are frequently used as “cleaner fish” to control parasitic sea lice in salmonid fish farms, but it has been questioned whether the benefits in terms of sea louse control outweigh the economic and lumpfish-welfare costs involved. Here we estimated the efficacy of lumpfish in controlling salmon lice ( Lepeophtheirus salmonis ) in salmonid farms by combining analyses of occurrence of salmon lice in stomach contents of lumpfish and experimental results on digestion time. We then conducted scenario simulations of salmon louse dynamics in salmonid fish farms, by combining the lumpfish feeding model with a lumpfish growth model and a salmon louse population model. Results showed that at a mean lumpfish weight of 50 g and typical conditions for other factors (9 °C, 2 kg salmonids, and 0.8 pre-adult and adult salmon lice per salmonid), the estimated feeding rate was 0.17 salmon lice per lumpfish per day (95 % confidence interval: 0.12–0.22). This rate increased with salmon louse concentration, temperature and salmonid weight and decreased with lumpfish weight. Scenario simulations of salmon louse dynamics under conditions representative for salmonid farms in Norway suggested that stocking lumpfish from the start of the production cycle with a 1:10 lumpfish per salmon ratio on average postponed the first salmon louse treatment by 43 days. The longest postponement was at intermediate external infestation pressure. Scenario simulations for a network of farms suggested that coordinated and strategic use of lumpfish after a spring treatment may succeed in supressing salmon louse outbreaks through spring and summer. • The efficacy of lumpfish as cleaner fish in Norwegian salmonid farms is estimated. • On average each lumpfish eats 0.17 salmon lice per day under typical conditions. • One lumpfish per 10 salmonids on average postpones the first delousing with 43 days. • Strategic and coordinated lumpfish use in an area may suppress louse outbreaks.