Observations in three areas in northern Tanganyika on the day-time resting sites of adults of Glossina swynnertoni Aust. showed that the most important of these was the underside of branches of trees. The number of flies seen on this site represented about one-third of the total population as calculated from the apparent density, and about half of them were on branches 4–9 ft. above ground, 1–4 in. in diameter and at an angle of less than 35° from the horizontal. It is suggested that were an insecticide to be applied to branch sites within these limits, then, since any fly must make six or more flights in the first 18 days of its life, it would be expected to alight on a treated surface at least once in this period. Were a lethal deposit maintained for twice this period, plus the pupal period, control could be effected.