In 1984–1985 insecticide-treated targets were deployed in the 600-km2 Rifa Triangle, Zambezi Valley, Zimbabwe. Trap catches of Glossina pallidipes Austen were modelled using a function combining logistic growth with diffusive movement. A simulation routine was linked to a non-linear least-squares optimization programme and fits optimized with respect to population carrying capacities, rates of growth and movement, and to levels of imposed mortality. In March–September 1984, the overall additional mortality was 2% per day of adult female G. pallidipes, increasing thereafter to 8% per day, due to the deployment of more targets, the onset of the hot, dry season and the ground-spraying of the adjoining Zambezi escarpment with DDT. For G. m. morsitans Westwood the corresponding estimates were 1 and 2% per day. For both species, the deployment of four targets km−2 in a closed population will ensure eradication. For G. m. morsitans a halving of target efficacy would reduce the killing rate to the point where eradication would be unlikely. Estimated daily displacements were c. 200 m for G. m. morsitans and 660 m for G. pallidipes. The lower rate for G. m. morsitans means that, while targets kill this species less effectively, re-invasion of cleared areas is slower. Targets do not markedly affect robust populations outside the deployment area. The Zambian tsetse population adjacent to the Rifa Triangle declined markedly during the experiment, however, suggesting that it is largely maintained by immigration. The methods developed here will be applied to data from other campaigns with the aim of improving the efficiency of tsetse control programmes.